Right now i'm really into Disgaea. (ps2 port)
It's a strategy game, with a hilarious script, and deep strategy play.
It's very time consuming since you can get your characters to level 9999 to max them out.
Other games I've enjoyed playing are:
Fighting:
Tekken Dark Ressurection - Great fighting game, lots of replay value
Naruto: Ultimate Ninja Heroes - It's pretty much the Ultimate ninja series for PS2.
Music:
DJMAX portable 1 & 2 - It's like beatmania. Which is really fun. (Import)
Gitaroo Man - Gitaroo Man series. It was on the PS2 i think.
Audition Portable - If you've played bust-a-groove it's kind of like that.
Patapon - Reminds me of loco roco, but it's about rythm and drum sequences.
Action/Adventure:
God of war: Chains of olympus - This is actually the first God of War I've played. It's pretty good. A bit short though.
Loco Roco - This game is kind of addicting. The background music is hillarious.
Ratchet and Clank: Size matters - I haven't played much, but it's pretty good. (first time playing the R&C series)
Megaman: Powered up - This is a great game. lot's of replayability and even a stage creator!
RPG:
Crisis core: Final Fantasy VII - Comming out soon. I've played the japanese version and it's great. It star's my favourite FFVII character Zack as well.
Shooting/FPS:
Metal Gear Solid Portable Ops (Plus) - The MGPO series is great. You spend most of your time building your army from enemy troops. Online is really fun.
Medal of honor Heroes 1 & 2 - A basic fps. good enough for Fps needs.
Syphon filter Dark Mirror/Logan's shadow - Didn't get very far into the game, but it's great so far.
I don't remember any others right now. I might post some more later.