Let's see, I'll avoid RPG's because to be perfectly honest I think you've played more than I have in the last decade.

Fighting Games: There are a number available. The most recent versions of Guilty Gear are on the PS2, Wii, and PSP. You can get any of the Street Fighter Alpha games on the PSP (though I think only Alpha 3 was specifically released for it, the others are on the PSN as PS One classics).

Action/Adventure: I'll go with Little Big Planet on the PSP. I just woke up so I can't think of any others at the moment.

Puzzle games: I'd probably only recommend Echochrome off of the top of my head, but it's a PSN only game. Can't really think of any others either.

Music/Rhythm: You may already have it, but if you don't then get Parappa the Rapper.