As you read this, remember I'm not angry, more just commenting on what I've seen. 
[I mention the remake, but really I'm mostly talking about house rules that have been floating around on the internet from the time before the remake came out, though they got a new lease on life when people started debating and comparing notes about house rules]
So if you look up "heroquest" online and if you start looking through forums and fan sites, you're bound to find them. Lists of homebrew rules, often copied from other places and I see very many common things. However for various reasons I don't use them. I have nothing against homebrews in general but there is a sense of the game I have that I find the most fun, that is largely based on nostalgia (and also simplicity) that prevents me from using many of them, though I do introduce my own. Each to their own. That said here's an ever growing list of common house rules for the NA/remake edition I see and why I don't use them:
1) Walk up to Chests to Open Them.
I think at one time I might have tried this, thinking perhaps it was what was always intended... that searching reveals what's INSIDE the chest and then you have to move adjacent to actually pick it up. I think when we went through this very brief phase, we also thought that you wouldn't spring the "trap" until you actually opened it. This is clearly NOT what the NA rules entailed, so I play it much more strictly now. You search the room, the first hero finds whatever the note says, everyone else gets a card. I suppose it builds up the suspense and might be a little more realistic but to me it just wastes time if there are more than two people playing especially so I'm not that interested in it. The japanese edition is the only version that explicitly intended you to do this, though it's quite possible (great recent thread on it anyway) that the original EU edition of the game might have had this "walk up to the chest" thing in mind, even if it's not really spelled out in the published versions. Interestingly enough it seems that the designers of the BQP/EQP/etc. were thinking of implementing it and even doing the "search each piece of furniture individually" thing too, but for whatever reason left that on the cutting room floor prior to release.
2) NERF (tm) Crossbow restrictions.
Many people find the Crossbow overpowered and seek to limit it in some way. This is the only reason I can conceive for doing this, but many give the excuse that it's "more realistic" the way they're doing it (and yet they don't change other aspects of the game that are equally or more "unrealistic" or historically "inaccurate"). For example many will limit its range, say to 9 squares. Why? I would point out that if it's a realism question, Crossbows of all sorts have been constructed and who is to say that you have a poorly made one that has such limited range? Look up world record archery, crossbow, etc. and even videos of amateurs shooting targets and you may be amazed what people can do. I like to remind people that you are HEROES not necessarily just schlubs off the street who just picked up this weapon for the first time. Another common limitation I see is that the Crossbow is two handed, so you can't use a shield. Of course there are videos pointing out that there are examples of warriors (and even amateurs) able to use a shield with another weapon, so this isn't perfectly realistic. It may take two hands to "load" the crossbow (pistol crossbows can be fired one handed) but there are also videos of even amateurs loading crossbows one handed. Why impose this limitation? Also many of these same people will respect the "intended by omission" rule (later explicitly confirmed by Avalon Hill on twitter) that a crossbow CAN hit the four orthogonally adjacent (closed diagonal) squares, making the Longsword less useful (I disallow this exception for that very reason, much simpler than adjusting the prices or trying to buff the longsword). I figure at the very least this is how it was played in the Japanese edition of 1991 (though this edition uses the "walk up to chests" rule and the "cards limit armory stock" rule which I don't use, so there). Also, it's perfectly realistic that you could shoot someone point blank with the crossbow yet they don't allow that, so what gives? It seems inconsistent to me, just a random reason to nerf a weapon that they buff in other ways ending up more or less in the same place with a very powerful weapon that is still fun to use. Another common nerf I see for the Crossbow is that the string "breaks" somehow, like if you roll two black shields. What self respecting crossbowman wouldn't stock a spare string and could re-string it very quickly? Also more importantly, How is this fun? So now you're going to be without this weapon the rest of the quest. Are you supposed to buy two of them just in case? I don't really think the idea of "critical fails" and "critical success" fits into this (d6) game but some people like it I guess. Next is the ammo. People say it's unrealistic for Crossbows to have "infinite" arrows/bolts so they insist that it "runs out." In a few expansions there are notes about crossbows you find that have limited ammo, but this is the exception. Again an attempt to nerf the crossbow by having it suck up gold. You can already buy multiple daggers to have a throwing supply but I guess this is just something I don't care for. Realism states that archers and crossbowman actually did bring quite a bit of ammo into battle during wartime, which would be quite enough for the kinds of usage this gets in a typical quest even without allowing for trying to "retrieve" the missiles from dead enemies (something that wasn't typically done in war, though was done in hunting and target shooting from what I've read). In wartime they also had soldiers stick extra arrows in the ground and even had men bringing in wagon-loads of spare arrows to keep them stocked. The idea of running out of arrows in a quest seems much more like a video game convention not something that enhances the fun here.
3) NERF (tm) Longsword restriction.
As if making the Crossbow more powerful wasn't enough of a problem some people want to nerf the Longsword as well, making it a two handed weapon that can't be combined with a shield. I guess they say this is more realistic because the term "longsword" (rather than side sword or arming sword) would refer to a weapon that would be more likely to be two handed. Using this logic the "broadsword" isn't a broadsword either, etc. I don't try to get that technical with my weapons. Whatever they are, or whatever they would have been called in medieval times is irrelevant to me. This is a fantasy game and it doesn't make the game more fun for me to introduce more nerfs to this weapon.
4) Limited Supply Armory deck.
For some reason people like to say that not only should you have Equipment cards for everything (I grew up with the Armory menu which has a lot of advantages, not least of which is that it's much faster to shop this way rather than shuffling through a deck of cards looking for what you want and the not having "enough" cards for everyone and constantly trying to print more and then having huge piles of cards in front of each person, which makes turns take longer, etc vs. a nice colorful board explaining what everything is with cool artwork) but that supply should be limited by cards as well! The only official version that limited supply based on cards was the Japanese edition. Even here though there was a reason for it.... you could buy healing potions (and to avoid making it too easy and having the heroes spend all their gold on healing, they limited the supply. Likewise in that localization the Elf couldn't wear much armor but he was the only one who could use the Crossbow. The strongest armor/weapon could only be used by the Warrior (Barbarian). That's fine. Having cards for everyone is nice, but I prefer the armory board. Plus you're just going to subtract the gold and write down the name of the weapon and how many dice anyway. I don't see why it's more fun if there is only one crossbow (again unless only one character can use it!). How is that realistic? You go from town to town and your money is no good.. you can't even pay a blacksmith to make it for you? Here is where having a video game format would be nice (or dry erase markers for blank cards)... if you want to vary the price and what's available between each quest. But since it may be a long time before you get to shop again, why would you limit the heroes so much? Not all of us have the luxury of relying on a regular play group that is going to be patient enough to go through dozens of quests with regularity.
[Edit: I should amend this because technically, literally, both 1st-1989 and 2nd Edition-1990 of HeroQuest did INDEED limit supply of Equipment based on cards. This was revised with the 1991 "Adventure Design Kit" box which provided a larger re-designed Character Sheet and instructed players to write items down on the sheet and that cards would not limit the available stock. Whether many EU players chose to adopt this official revision is unclear. But supply for Armory or Alchemist Shop items was never limited in the NA edition and explicitly is not limited in the remake edition which adopted the Equipment deck mechanic alongside the Armory concept].5) Limited carrying capacity.
I see this one less often, but this is another video game convention... that is, people say it's unrealistic for you to be able to hold "all those weapons" and yet they still give you a pretty absurd carrying capacity. As people on youtube like shadiversity have pointed out, how realistic is it to have an adventurer roaming around with 500 gold coins in his pockets, and a bunch of potions that he won't be able to get out and drink in time to avoid dying, and a suit of armor, and a bow, etc. and somehow because you limited him to two swords, that makes it more realistic? Sorry, I don't buy it. No magical "bag of holding" required, I just play the game the way it was designed on this point. You can write it all on your character sheet and if you don't want something, you sell it off or give it to another hero or drop it in a dark corner of the dungeon and forget about it, whatever.
6) Plate Armor is too slow.
Here I can sympathize with a lot of players. People love having plate armor but they HATE that it slows you down. Many will say sure it still slows you down but not nearly as much. Maybe it just subtracts a couple of squares of movement (like only 2) or they say that based on your "character class" (pet peeve, they are character types, classes are a D&D term mostly) like maybe a Barbarian is slowed down less than an Elf. When people bring up realism however I laugh. How is it "realistic" that a Wizard can't wear it? The realism people go all over the place claiming you needed a squire to put the armor on you (not true, and there are videos of amateurs putting on plate armor un-assisted, or even very quickly assisted). Real medieval plate didn't require you to be hoisted onto a horse with a crane, and you could run and jump around. Yes, jousting armor was a lot heavier and some of it quite restrictive, but whatever. You could just reason whatever this armor is, it slows you down. I don't mind it being that way and having a Knight that wasn't slowed down by it at all kind of rubbed me the wrong way at first but it doesn't seem too bad overall. There are a lot of ways to speed up a "slow" character with magic, so I don't consider this too much of a big deal.
7) Potions expire.
The NA heroquest is sometimes mocked by fans of the EU edition as "potion hoarder edition." It is that, but later quests are so difficult that it kind of makes up for that. Why hoard potions? Because you aren't allowed (at least until the remake) to sell them back to the Armory to get some gold back. Players don't just use potions to use them up, they keep them forever unless they are forced to use them, it seems. Heroes buy potions without knowing what they will actually need if it's not just plain old healing. The idea that these potions are now going to be worthless to me is just annoying. Maybe if they said potions you buy don't expire, but that's much more to keep track of. Yes, the EU edition cut you off from treasure potions (and had no potion buy ability, only Against the Ogre Horde had some special large potions if playing the campaign "as a series"). I just think it's more needless complexity and I don't care if people have to write on the back of their character sheets. Use your potions or give them away if you get annoyed I guess.
8) Monsters are boring and weak, give them unique abilities.
This is kind of a cool idea, wanting to give monsters special skills so they aren't boring. To me this is just more complexity though. The whole point of having quest notes is so that you can have special monsters... give them names, give them magic, play around with their stats, etc. but saying every Orc has this or that skill, and there are four different types of Chaos Warriors based on a different Chaos god they worship, while interesting is just a lot more work for Zargon to do, etc. I have no problem occasionally introducing some tougher monsters to keep it interesting like giving diagonal or ranged weapons to ordinary monsters or buffing out the odd mini-boss with some extra attack/defense or a spell or two. I just think some of it is overkill. Plus, whatever happened to having some generic monsters? If all goblins have X and Y abilities it's no longer unique or special.
9) Dwarf and Barbarian are boring, give them cards!
This I can sympathize with. So many other new heroes are given fancy spells and special abilities so these two "tanks" start to look boring by comparison. Unpopular opinion here but what's wrong with "boring"? Simple means that these are great heroes for new players to start out with. Maybe I don't want to manage a big pile of cards. Not everyone wants HQ to be more and more complex. Relax! I too have decided to allow them to pick up some Combat Cards between quests, but I still try to keep things simple if people want it that way. Many starting players don't want to be the Wizard because it's daunting to have 9 cards to manage (and those turns are going to take a lot longer than the guy who has only to search and fight).
10) Searches! People can't decide if they want them simpler or more complex, but they never really save time...
On the one hand there are people who hate that searching is split into three actions. They want it to be two (like the EU edition) or just one! They say this speeds up gameplay. Okay, but then often they turn right around and say you should be able to search each individual piece of furniture which is going to make things take a lot longer, plus it puts more pressure on Zargon who now has to write in all those extra things (since most pieces of furniture have nothing in them... it's Treasure Chests and sometimes the Weapons Rack, and more rarely the Sorcerer's Table or Alchemist Bench or maybe the Bookcase, usually furniture is just space-filler decoration). Then they will object and say it's "not realistic" that you searched the whole room and stopped when you found one thing and there's no way the other heroes would find anything so they want it to be one search per room, period. So now you've greatly increased the difficulty because now you have 1/4th the treasure and even more opportunities for the heroes to "fight over" the limited resources. So you fix it again by increasing the amount of loot that is found in that one search per room... what problem did you solve again exactly? I find that heroes enjoy the opportunity to start building their own stash. It's one thing if you're a single player controlling multiple heroes, but it takes some of the fun out of it if just everything is handed to you (unless you're humbly sitting through your first training session I suppose).
11) The Wizard sucks. Buff him!
Yes, everyone agrees the Wizard sucks (or something) and needs to get on the Charles Atlas steroid program at the very least. They want him to be as powerful as the Barbarian, so he can win quests single handed. I can sympathize with the love of the Wizard and wishing him to be better. This isn't Gary Gygax's fault (supposedly he hated wizards because at his table the they were "too good" I'm not a D&D historian, go ask one). And I don't care if Gandalf dual wielded a sword and staff while throwing fireballs at dragons either. HeroQuest is making each of the heroes unique and they are supposed to (in this version) work together to accomplish the goal. Yes, you could modify the Wizard so he is a tank who needs noone, but then why do that? Now you don't need the other three heroes. Yes, many complain that he has body points that are too low (the Wizard quest pack was going to give him an artifact to remedy that but he had to earn it). Yes, there were going to be special potions only he could use, in this unreleased pack. Yes, in the EU edition he can use magical armor and magical weapons. And if you want to see what it's like if you just go all the way, check out the official 1991 Gremlin HeroQuest PC game. In that one the Wizard can wield a battle axe, while wearing plate armor and fire the crossbow, etc. He's not limited by gear in any way, making him a weaker Barbarian with magic. How about something that gives him unlimited spells? Okay that's cool, but now why would he do anything else but spam spells? I guess that would be fun at first just like it's fun to play an FPS game in "god mode" for a few minutes after you're tired of losing, I get it. I just don't mind that the Wizard isn't almighty. Once he's tricked out with his Wizard artifacts and buys bracers (which he didn't have in the NA edition) he's not so bad. Most quests are designed for the four heroes, not for a solo hero. Yes, Prophecy of Telor has some cool ideas that can buff the Wizard (doesn't have to be the Wizard) and make him the "star" of the story, but it's still not a solo campaign where one Hero has to shine above all others. The barbarian and dwarf are awesome, but without healing they eventually die like anyone else. They are weak against magic and later quests where mind points are basically your health makes them absolute weaklings compared to the Wizard.
12) Door blocking sucks, how to stop it?
Even Avalon Hill is getting on this train and I can sympathize. It's "boring' For Zargon to always face the same strategy that the Rulebook TEACHES YOU TO DO which is to have a strong character block the doorway and have other heroes with diagonal attacks flank him and take out the monsters. This is just something "cheap" that is part of the game and frankly good strategy, much like Zargon moving his monsters around strategically instead of just having them dumbly run forward and attack the closest hero (rather than attack, move him out of the way, move the next monster in, force them into traps, etc). Zargon gets the cheap move of traps on the other side of the doorway and the last hero in the round searching for treasure and getting a wandering monster that attacks him and then Zargon's turn is next and he gets to attack him AGAIN, so there. This isn't Space Crusade where the GM is expected to have an equal chance of winning and is always actively competing (even though this is a debate.. whether he's more of a referee or facilitator or if he should actually try to make it hard to win).
13) Permanent Death.
So many people complain about this, again many who prefer the EU edition where once you got to zero body points that's it. Here's the problem though, if you get rid of death saves, what happens? On the next quest that player just comes back with another hero who is the same exact hero just with his name changed (at best) and starting gear again. Are you really going to ban someone from the table because their hero got killed (maybe especially because their teammates didn't help them out or they were new and didn't know everything yet?). Seems like a poor idea. Just as I wouldn't love a video game that deleted itself if you lost one time (and I don't care if in real life you only live once, that's not the point of games.. what is this, russian roulette?? that's not fun, that's torture/execution/suicide!). So I have no problem with last minute death saves from those potions (the ones people complain that they are stockpiling) finally getting used, or elixirs of life needing to be found to revive that beloved character (people get attached to their heroes believe it or not even though it's little more than a hastily thought up nickname on a piece of paper). Sure I guess you could force someone to play a different hero, but at a certain point it's already bad enough they lost, now you're going to punish them, this will make some players just not want to come back (not saying you should coddle sore losers either, just saying, especially if you're dealing with younger/new players this isn't usually that great... what is this, Dark Souls??).
14) Getting rid of roll to move!
I loved BardicBroadcast's meme video too, but why is getting rid of roll to move better? It's like people who insist that modular dungeons are always better than the HeroQuest dungeons. Just because you are more familiar with that, maybe? But rolling dice is fun. Flipping over cards is fun. Maybe to some people just always moving the same number of squares or looking up tables is more fun. Some people think it's boring to roll a die that only has six sides. I disagree. That's the game we grew up playing and I still like it. Each to their own, but even when I do allow heroes to not have to roll to move, THEY STILL USUALLY JUST ROLL TO MOVE (again because rolling dice is fun). Now if I'm Zargon and I'm rolling all the dice for me and for all four heroes, that can get a little much on those long campaigns, but usually rolling dice is one of the few actions a person gets to do on our streams, since we can't all be at the same table at once. You could give the heroes unlimited movement for all I care, but it usually just means they're in too much of a hurry anyway (how is getting 4 squares automatically that much fun for a hero?) and will run straight into traps/rooms full of monsters.
15) Paying for upkeep, taxes, etc.
I see this less often but I also see it suggested a few times by various people. While the whole idea of adding a more varied and deep roleplaying experience kind of sounds fun at first (and I'm sure it has something to do with other RPGs people enjoy out there like D&D) but to me it gets in the way of the action. HeroQuest is about exploring the maze, getting the treasure, killing the monsters and taking home the glory (if you can live to tell the tale!). To me the gold you get paid is pure profit that is intended to upgrade your equipment between quests (and later, to hire mercenaries and buy potions to keep you alive for the even harder quests ahead). The idea that the Emperor pays you a salary or you make money on your side gig is kind of cool but ultimately all of that other expenditure is boring. Sure, we can assume you have to bath, go to the toilet, repair your gear at the local tailor not just the blacksmith shop, eat, sleep, go to therapy after the horrors you've witnessed, visit friends and family, etc. but all of that can happen off camera and in the end whatever money you spent or got evens out so you're back to spending the 100 gold you got on the last quest to put towards that new weapon or piece of armor you need for the next one. Maybe some people enjoy that other stuff but to me it adds needless complexity. Some have suggested gambling for more gold between quests (the Japanese edition used this to level up rather than get more gold) or maybe paying to store excess gear, that's fine, but I think the other stuff is overboard. At some point you're just making your own game with the HQ assets as markers for your AD&D or pathfinder campaign (which is fine, just not my cup of tea!).
16) Dice rolls for simple actions.
This is more just a general pet peeve. Some people like dice rolling so much (or they just got rid of it by eliminating "roll to move" so they want some of that back) that they want you to roll dice for stuff you normally don't have to roll for. What would be the extra fun in rolling to see if the treasure is not really treasure, or whether you can retrieve something on the ground that you're trying to pick up or if the spell you're trying to use works (usually it just WORKS and the only rolling is to see if the enemy can resist it, which to me is all the complexity you really need most of the time, or maybe with a summoning spell to see how many creatures are summoned this time). When it comes to random events I'd much rather draw a card than consult a table or (frankly) roll yet another die. Keep it simple. I don't mind certain actions being "free" with a guaranteed outcome. I think this is a strength of the game, not a weakness. Others disagree.
17) Zargon sucks, get rid of him!
Why do people love (true) solo quests so much? Yes I sympathize if you have "no friends" or your family is sick and tired of playing "that damn game" one more time... but to me playing Zargon is FUN. Apparently even Milton Bradley thought people wouldn't want to be Zargon so the original edition had you rolling dice to see who drew the short straw and "had" to be him (Morcar in that edition). Hasbro continued the trend through Avalon Hill's "Board Game Companion App." Let me tell you it shows. No matter how good AI gets these days, the automated Zargon lacks creativity, and he's rather annoying (though kudos for getting him to work at all, to the designers). Being a GM is so much fun especially in HeroQuest where 99% of the work is already done for you (and riffing and improvising once you get the basics down is tons of fun). Yes, it's nice to be able to play as a hero for a change, but most of the time I would rather be playing with a human GM who loves the game, rather than a computer or drawing random cards only to find myself in some room that makes no sense or is dull and boring. I've tried various ways of playing solo, and while some of them are interesting (like having little tiles moving around like the blip tokens in Space Crusade) I think it really detracts from the enjoyment of the game. Yes, occasionally you'd have a bad experience with some GM but usually it's fine, if not great. If you've only ever played HeroQuest Solo, I feel for you. Get to a game shop or hop online and setup a game... it's SOO much better. This is how the game is meant to be played! If I want a solo quest I'm more likely to just fire up a video game anyway, personally...
18) No shopping allowed!
This often comes up with Kellar's Keep but can also be applied to other quests. Again citing "realism" people say they don't want to let the heroes "go shopping" between quests. This takes a lot of fun out of the game because now you're (even more unrealistically) carrying around hundreds or thousands of gold coins and with no way to spend them. To compensate for the boredom of no shopping now Zargon is modifying the quests to add more gear and potions to find, maybe adding traveling merchants, etc. and you're right back where you started all because you found it "unrealistic" that they could exist this particular dungeon and visit an armorer or alchemist to get some stuff then head back to the next leg of the journey. I think at a certain point you might as well ask why the Empire didn't just outfit you all with the gear you needed from the start and having porters carrying your extra gear the whole way? The point is that the game gives you a sense of accomplishment as you progress and earn things and increase your power as your challenges increase. It's a natural enough thing to enjoy this, so I don't see the improvement in fun by taking it all away just because "it wouldn't make sense" that you'd step away from the mission, even though some quests explicitly write in the setting that it would make perfect sense (for example in Frozen Horror quests take place near towns and villages or else it's implied you would have left and come back to deliver a prisoner to safety, etc. so plenty of opportunities to shop even if it's such an "urgent" mission, etc).
19) When the action stops, the quest is over.
This is more a question of quest design. Many players are too impatient. Any backtracking or periods where there is no combat or a big treasure being found and they get antsy. Unfortunately there are some classic quests that end with a "slog to the stairs." If this were a video game you wouldn't get to complain because the game would force you to move to the exit even though you've "accomplished your mission" (even though part of your mission was to get back to the stairs alive, not just kill the bad guy and find the artifact). Still, this is another reason to have a live Zargon, because you can beg and plead (hopefully not whine and complain) that it's "so boring" and just have him end the quest right then and there. As kids we had more patience, dreaming about the stuff we'd buy with the gold we found and doing a "victory lap" to the end (plus, rolling dice is fun). I can sympathize with a lot of groups especially if the quest design is wanting and people are tired at the end of the night, etc. This is one of those areas where I'm kind of annoyed but I can roll with it so I have done this on occasion or modified the quest to try to have "non-stop action/threat" to keep things going to the bitter end.
Any others I missed? Maybe Dual Wielding (cool idea, but does this mean you get double attacks every turn now just because you bought another weapon)? Again, not to berate anyone who loves these rules, exercise your freedom and have at it! I don't mind at all that there are two dozen or so expanded Armories out there and they all pretty much feature the same weapon options (bastard sword, great sword, short bow, long bow, cloak, bracers, spear, halberd, rapier, sling, war hammer, throwing axe, tower shield, buckler, boots of speed, and usually some type of magical armor or magical weapon intended for the wizard, or even some kind of "leveling system" you can cash in with gold). Or they give you potions that just let you break rules (a potion that lets you use a shield and battle axe at the same time, a potion that lets you move/disarm traps/etc without rolling or lets you do part of your movement and action and then the rest of your movement... I'm surprised I haven't yet seen a potion that lets you move diagonally or search a room that you're not in at the moment! that's fine whatever people want it's just something I would rarely do that blatantly).
I know I can be hypocritical on some of these things. Sometimes I care more about realism in one area so I'll change it, while leaving something blatantly goofy in another place well enough alone. Sometimes I'll sigh at the people who buy unique miniatures for every character, and meanwhile I own some unique minis that I like to use for some of those occasions (just as I like to print new cards, I also am fine with other things just because a line of text that you write down). We're still having fun talking about it, right? And if I'm at your game table and you play this way, I'm not going to argue (at the table). And what's with people trying to build 3d dungeons? 3d dungeons look so cool! But good luck storing them and re-arranging them for each new quest (if you can, more power to ya, I'll admire from afar for now!).
= one hit
= one hit & pushback
= cancels one hit
) or things like that and then using them to kill bosses or tough rooms without effort. There is room for argument that they should be able to do that realistically and part of the fun can be had in those moments.. but ive found its very easy to cheese the game this way, and allowing my players to do it has had them burn out fast in previous campaigns.. so ive taken steps to make it harder