Everything; RPG, racing, adventure, FPS, 3PS, horror, action, top down, roguelike, sometimes even sports games. The only games I'm not too keen on are JRPG's and turn based games, mostly because JRPG's are usually turn based.
My favourite franchises are Silent Hill, Dead Space, Half Life, Uncharted, The Last of Us (not a franchise just yet, but here's hoping), Little Big Planet, any Mario games, early Sonic games, Burnout, Gran Turismo, Bioshock, System Shock, Deus Ex, etc., etc.
Basically, I like all games, but some of them are kind of disappointing.
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Such is life, that expressing yourself and the truth has you berated.