Most fighting games. More specifically, fighting games with health bars and those weird combo moves; thus, wrestling games and Super Smash Brothers are still fine by me.

Most real-time strategy games. I'm just not very good at them. I still try them out from time to time and have even enjoyed quite a few - Warcraft 3, SpellForce 2 and Ground Control spring to mind - but most of them I can't tolerate for much longer than an hour or so. Doesn't stop me from trying, though.

Stealth games. I suck at every single one of them for some reason, and even mandatory stealth elements wind me the fuck up. For instance, the stealth missions were the last nail in Ring Runner's coffin for me, although I was plenty annoyed at the game even before that.

Roguelikes. I do sort of like some of them, but many of the features that the proper target audience finds desirable simply annoy me.

Modern first-person shooters. I can take them to a point, but pretty much everything since F.E.A.R. is simply too homogeneous and dull for me. I'd take Marathon over Call of Duty any day without a moment of hesitation.

Sports games, excluding motorsports. Just not interested in sports in general.

Anything that is either a "Diablo clone" or "the game that Diablo III should always have been". Oh, boring grindfests. Count me out, then.

JRPG's, with the exception of Chrono Trigger and another game that I just can't remember at the moment. The design is generally too over-the-top, the writing poor, the characters unlikeable. Soundtracks tend to be fantastic, though, I have to give them that.

EDIT: Also, anything with a multiplayer focus.