I like FPS/shooters foremost actually, even though I'm not good at them in the competitive realm (like online CoD). I dislike MMOs. They really feel like a waste of time and a chore to play. RTS is ok, use to love Age of Empires II.
I do like RPGs, just mostly pen and paper ones. RPGs I've liked in vidya format: Icewind Dale series, Baldur's Gate series, Temple of Elemental Evil, Knights of the Old Republic, etc.
NF here, and I really, REALLY like fighting games. All the action and reflexes needed makes me excited. The idea of two guys standing against each other to find out who is the best is great.
I've never been too much into RPG games (but I couldn't escape Skyrim charms), Shooters (specially fantastic ones), Racing (as a kid I used to play Gran Turismo, not anymore) and sports (here in Brazil soccer games are absolute, and I hate soccer). As a Ne dom, games where I can explore my imagination such as GTA series, Minecraft and open-world games get my attention easily, but these games for some reason doesn't keep me for a long periods of time.
Multiplayer games, and not online multiplayer, split-screen multiplayer is extremely fun for me, being co-op or versus. God, I could never measure the amount of fun I had playing N64 Mario Party series, GoldenEye, Crash Team Racing, Def Jam FFNY etc etc
It's hard to say about adventure games, because this genre is very wide. But unless the plot is really captivating, I don't like them. Unless it's a Survival Horror adventure...