The only kinds of games I really don't like are platformers (boring), and puzzles (even worse). I also don't like games that require a walkthrough to beat, i.e. Myst. I like games that have high-level action (i.e. Uncharted 2, Halo Reach) and action RPGs of any type (i.e. Oblivion, Tales series). Also, if a game has girls in it, they MUST be beautiful. I modded Oblivion heavily just so that the villagers would look a little better.
I'm not sure I like static, turn-based fighting. That means most of the FF games. It's just too slow-paced for me. If a game's turn-based, it must have other options during battle, like the newer Mario & Luigi games on the DS.