Where do I even start? Final Fantasy X, Sly Cooper 2, Ratchet and Clank: Up Your Arsenal, Final Fantasy XII, GTA Vice City, Kingdom Hearts, Jak & Daxter 2, Dark Cloud, Rogue Galaxy, Okami, GTA San Andreas, so many classics and under appreciated gems!
I think my all time favorite PS2 game would be FFX. Nostalgia plays a huge part in it, but it was one of the first games I've bought and beat on PS2, and it got me hooked onto JRPG's.