Survival, Sandbox, RPG, Strategy, Puzzle, Platformers...
Man, I just can't choose. I love most genres, though I personally tend to avoid horror anything because I'm not a huge fan of it.
RPG's, adventure, fps, strategy, puzzle... I'll play anything really that looks good. Typically anything with a good story/lore is something I will go for.
Not mmo's though. Never enjoyed them for some reason, not my kind of game.
action/adventure, platformer, survival horror(preferably where the hero isn't a gun-toting bada** and there's more emphasis on the puzzle/survival parts and less on the action) and probably that's about it unless I can think of something else.
I find that I like a good amount of RPG games. I'm more into rpgs (I think its called Sandbox RPG?) where you can explore, make choices and customize. I also do enjoy puzzle games (to an extent, definitely not anything like Myst) and on occasion FPS.