Turn-based RPGs (exceptions: Mother 3, Mario RPG series) FPSs (exceptions: GoldenEye, Perfect Dark, BioShock) Sandbox games. I've bought every major GTA title since GTAIII (including III, Vice City, San Andreas, IV, and Chinatown Wars) and I have yet to enjoy any of them. I do want to give CW another shot though. RTS, sports games, realistic racing games
fighting games (hugely not into them. I suck at all of them, and I don't like things I suck at. But there's an exception: Super Smash Bros. for the most part, even though I'm not as into it as I once was)
FPSs (this is the closest to changing as of late. I enjoyed Half Life 1 when I played it on Steam recently, and I've always liked Doom from the first time I played it. I don't really like the progression in Call of Duty: Modern Warfare though, and it's my understanding that a lot of games take inspiration from Call of Duty, so it makes me hesitant to check out more FPSs)
sports games (I'm not into sports in real life, so that extends into my lack of interest for video game sports. I don't even know the rules for most sports, and I don't feel like learning them just to be able to enjoy some random sports game. Exception: most Tony Hawk games. They have an arcade-ish scoring system and just enough "gaminess" to them to keep me interested. Plus I actually skated for a couple of years as a preteen, so I have an idea of what it's like, and I appreciate the over-the-top quality of the series in comparison to how skating actually is in real life)
3D action/brawler games (Devil May Cry 3 hasn't caught my attention the few times I tried it, I can't stand MadWorld, and I got fed up with the Bayonetta demo really quickly. A lot of it just feels too shallow for me to keep playing. Exception: No More Heroes. I like exploring the overworld and doing side-jobs amidst all the action. This is part of why I don't like the sequel as much. Also even though you could kind of consider it an action-RPG, I really like Yakuza, partly because it's not just fighting bad guys. If you went through linear stages fighting with Yakuza's combat system as it is, with none of the side-features, I would most likely get tired of it)
Don't really have much experience with RTSs aside from Little King's Story, but I put that game down after a day or two, so maybe I'm not really into that genre either.
I was going to come in here and talk about a few genres I don't like that I've complained about over the years, but I realized that every genre I've ever not liked I've suddenly developed a test for in certain aspects over time...
I honestly can't think of one genre I don't enjoy playing.