I like playing gangster video games. I've played Scarface: The World is Yours, Godfather, Mafia, and Grand Theft Auto: Vice City on PS 2. Currently, I am playing Crime City on facebook. Not a great game but a good way to pass the time.
I also like playing the Street Fighter: Alpha games.
I enjoy pretty much all kinds of games, but I guess I have to lean towards shooters. Gears of War, Call of Duty, Battlefield and so on. I do like certain RPGs, and I don't think i could live without NHL.
I like music video games (Guitar Hero, Rock Band, Rocksmith), extreme sports games (Freekstyle, Downhill Domination, SSX), and fighting games (Mortal Kombat, Virtua Fighter, Dead or Alive).
I love all game genres equally except for rhythm games, but if I had to choose I guess I would say FPS. Its the closest to actually feeling like you are part of another world given the camera perspective.