Genres I don't like:
Bethesda RPGs - somehow they messed up my favorite genre. That takes talent.
FPS - I just don't like the first person perspective. Games like Mirror's Edge fall under this too.
Realistic Sports - Madden, FIFA, etc....
Puzzle Platformer - This is a good way to mess up a platformer game.
Genres I really, really like:
RPGs - my favorite genre overall except the Bethesda ones
Turn Based Strategy
Tactical Games - RPG or not
Open World Action
2D Beatem Up
Rhythm - especially if they have instruments
Arcade puzzle - e.g. Tetris, Katamari, etc...
Genres I sometimes like:
3rd Person Shooter
3D Beatem Up
I think the only genre I haven't tried is MOBA. Most of those are on mobile platforms which I usually don't fool with.