As primarily an RPG fan, I have very few complaints about other gameplay styles/types. So my list will be primarily focused on said genre. That said:
*.) Battle or equipment systems that work against themselves. Example: Rogue Galaxy. I love Rogue Galaxy, I really do. It's an absolutely wonderful game with an involving storyline and plenty of useful and fun innovations. However, I have one problem with the game system as it is set up: they have this wonderful weapon growth system whereby the longer one of your characters uses a certain weapon, the stronger it inevitably gets. It's also wonderful how you have this neat item/weapon combination system where you can get certain weapons only after leveling them for a certain amount of time. Problem? Each weapon's levels are unique to that particular instance of the weapon, meaning if you accidentally drop or merge the badass sword you've been working up you have to start levelling it all over again from scratch; also, when you decide that it's time to upgrade to a new weapon you feel like you just wasted a good amount of your time levelling up your past one only to throw it away, knowing that you'll never be able to see it again without spending more time levelling up an identical weapon. Combine that with the massive number of weapons in the game and you basically never really USE or care about the weapon level-system unless you're trying to make a particular weapon from combinations.
*.) No healing outside of items. Example: Rogue Galaxy again. I don't mind it so much as the previous entry in Rogue Galaxy's case, since every save point effectively serves as a shop and you're basically rolling in dough from the first stage onwards, but it's really annoying knowing that I HAVE to use all of my potions, since I don't have a character who can heal my party for me instead.
*.) Active-Time Command Selection. Example: Final Fantasy (almost all). I really don't mind active-time battle systems so much; waiting for the bar to fill is not a HUGE exercise in patience for me. However, I wish that when a character's turn came up combat would freeze while I made my command selection. I hate feeling rushed through the menu commands, and even the "wait" mode doesn't entirely eliminate this problem.
*.) Abilities that LOSE attributes as they level up. Example: Final Fantasy (many). Remember FFVII? Did anyone ever level-up the Slash-All materia? It was kindof cool how it turned into that attempted instant-slaying attack against all enemies, right? Generally, yeah. Until you tried to use it against a boss with multiple attack sections. Then you basically have LOST the ability to attack with that character. Annoying as hell. Most major game companies find ways to get around this type of thing, but it's still annoying.
*.) Taking character customization to such an exteme that characters lose a sense of personality. Example: Final Fantasy (most, except IX, and to a lesser extent X). Call me non-creative if you want, but if I'm gonna control an entire party of characters, then I want to feel like their personalities are reflected in the battle system, at least a little. Games like FFVII, FFXII, and Tactics, where every one of your multiple characters can go in any direction you choose, make me feel more disconnected from the characters, since I only see what kind of person they are during cinemas and cutscenes. It also makes me feel like I'm creating more of the story, which isn't so bad, until I GET into a cutscene and remember that I'm not. Now I'm not saying that open-ended character customization doesn't work, because it does; however, it works best when you have only one character, not 4+ (such as in Vagrant Story), or if the customization options are not absolute and total (such as in Breath of Fire III and IV). I know not everyone will agree with me on this, and that's cool. It's just my thought.
*.) Permanent detriments for temporary failures. Example: Fire Emblem series, Dungeon Lords (PC). It annoys me like nothing else how some games will permanently penalize you for character death. In Fire Emblem, if one of your characters dies, they are gone for good. Period. End of discussion. Start over the game, because you will never see them again. Granted, that's realistic, true, but I'm not playing a video game for realism. Similarly, in a little-kown game called Dungeon Lords, whenever you die you permanently lose one point on one of your stats and the Experience Points that you had earned towards your next level are lost; I don't want to do the complicated explanation of the math involved, but basically a Maxed Out character in DL who has died less will be more powerful than one who has died more. Major, major suckage. Makes me just not want to bother with it at all.
*.) "Beat the Hidden Secret Ultimate Boss in order to get the main character's Ultimate Weapon." Okay, so once I've beaten the secret hard-than-the-final-boss Secret Boss, what's the point in having the Main Character's ultimate weapon? Legend of Dragoon was smart about this; in that one, you had to UNLOCK the ability to fight the game's Secret Boss basically by completing the longest side-quest in the game, so fighting the boss was basically your reward for blinging out your characters with all the best shit. THAT was a good idea. Getting the main character's ultimate weapon and never having anything to REALLY use it on? Not such a good idea.
Okay, that's all I've got for now.