I only own three games now: NBA 2K6, Shin Megami Tensei: Nocturne, and God of War.
If you like basketball, the NBA 2K series is top-notch, in my opinion. More simulation-esque and less arcade-like. If you like RPGs, SMT: Nocturne is absolutely amazing; the only catch is, you may not be able to find it very easily (eBay has new ones selling for like $80 and some used copies are going for just as much) because it was one of those limited release US versions of a popular Japanese game. Someone already mentioned God of War, but it's a super-fun action/semi-RPG.
I know there are lots of others, but I haven't kept up with PS2 games in a while myself. I mean, I only own three...
