In fighting games: Combos that require you to press opposite directions one after the other, for example, Circle. I ALWAYS press down or up without wanting to and I screw up most of my combos when they introduce commands like that. So in most fighting games, I end up using like 1/8 of the original roster because I suck with the rest.
In FPS: Infinite respawn missions. I always take like 10 minutes to realise I'm stuck in an infinite respawn area. They should totally get rid of them once and for all.
In RPG's and RTS's: TOO MANY STATS. I consider myself a "hardcore gamer" but when it comes to games that have massive amounts of information on screen, I just can't deal with it. I just use the easiest way to beat the level and move along.
That's what I suck at, but I've been reading other posts and I share most of those experiences. Lack of engagement towards a game due to X mechanic they included, stupid AI, bad dubbing (I live in Spain, almost every game comes dubbed and they reuse the same actors over and over, gets old really fast, not to mention those games that just have terrible dubbing, ahemkillzone3ahem), etc...
Also when I was a kid, I couldn't stand games that would throw paranormal enemies at you out of nowhere. Like, you have your typical shooter, you are enjoying it, and all of sudden it becomes a survival horror and you have to shoot down zombies (Far Cry 1, one of the older Red Faction games, Perfect Dark...)
Now I have grown up I understand why do they do it, so the games gets progressively harder and more of a challenge, and I appreciate it. I am also not so easily scared with dark games so that might help too. Still can't play Amnesia for 40 minutes or longer tho...