I like open-world RPGs and simulations the most. Not so much because they put me myself there, but because they let me invent a character, think of a past and a personality for them, and grow attached. Creating lives and stories in my head is a great point of enjoyment for me for whatever reason, so I don't ever really use those genres as a conduit to channel my own personality...every time I play a new game or a new character, I'm someone new, and I make different decisions based on that. I think trying to think outside of myself in that way is what makes those genres the best for me.
But really, I'm fond of most everything. Platformers are something I'm getting much more experience with now that I have an XBOX controller to use alongside my PC. One genre that I didn't think I'd ever enjoy and ended up falling in love with was the bullet hell shooter (danmaku) style of game. Strategy games like Tower Defense and good old-fashioned battle-of-wits type games such as chess are right up my alley, also. Truthfully, the only genre I can never get into is FPS, and that's a little more because I'm woefully bad at playing those types of games than because I fault their design.