I'll support a few other suggestions in this thread, and make some more.
God Hand is an absolutely zany and fun third person brawler that you won't regret picking up.
Dragon Quest VIII: Journey of the Cursed King is probably my all-time favorite RPG, and it's probably nostalgia talking, but everything about it is just perfect. I bought it three times. If I still had a PS2, I'd be playing it to this day.
The Sly Cooper series as a whole is great. Not your standard stealth games, and the missions and characters will keep you hooked.
Call of Duty 3 is something I replayed tons of times, and it's a pretty goddamn good shooter for it's time. Same with the Medal of Honor series, like Rising Sun. Double the fun if you have another person to play through the story with.
Dragon Ball Z: Budokai Tenkaichi 3 is a must-have if you're a fan of DBZ or just fighting games in general. Budokai 3 is great to pick up as well, unless you don't mind the fact they changed all the music for the HD Xbox 360 release.
Gladius is something that I don't think alot of peple know about/had, but I thought it was a nice turn-based strategy (like Final Fantasy Tactics) set in not!Ancient Rome. You go around the world and fight through several gladiatorial arenas, but with plenty of other things to break the monotony.
Final Fantasy X is my favorite 'main' Final Fantasy, and always will be.
Robot Alchemic Drive if you want a 'so bad it's good' dub and giant robots duking it out. And you get to control one from the ground!
Grand Theft Auto: Vice City and San Andreas are classics and nothing like GTA4. May or may not be a good thing for you.