.hack quadrilogy,Drakengard 1 & 2, Resident Evil 4(or for GC), Final Fantasy X & XII, GTA: San Andreas, God of War 1 & 2, Star Wars Battlefront (only the first in my opinion is worth getting), Shadow of the Colossus (surprisingly refreshing), and Chaos Legion(repetitive but it still amused me)                                                                      

My favorite character from a PS2 game would have to be either Chaos Legion's Sieg, Final Fantasy XII's Balthier, or Drakengard's Caim.

The best cover art on a PS2 game would have to be Drakengard in my opinion you could judge that game by it's cover.