Adventures
Action/Adventures
FPS
Platformers
They're the main genres I'm interested in. It also depends on the gameplay mechanics, the story (or lack of) and characters, themes, and any sub-genres that may be mixed in. For instance: I love a good FPS or Action game when a good story is involved, which deals with mature themes (BioShock, Grand Theft Auto, Red Dead Redemption), and the game's sub-genre(s) are either horror/survival horror, crime drama, fantasy, mystery, puzzle solving/investigating, or a character's own personal journey of self discovery...
I can't say I'm into RPGs though, I'm afraid. It's strange considering how much of a geek I am.
But I just can't get into them. There are a handful of games I do like that have RPG elements though, but not many. But if I had to choose between a Western or an Eastern RPG, it would probably be the latter.
And here's someone else who's not into Strategy games either.
The only one I enjoyed playing years ago was The Settlers III.
And a big no-no to sports, racing and fighting games too.