The PS2 was such an awesome console, and I can't possibly come up with an all time favorite.
The Ratchet and Clank series comes to mind; those games were so good! The platforming was tight, the weapons were unique and different, and the shooting was good for a game of its genre. I wish the modern Ratchet and Clank games were as good.
Rockstar killed it during this gen, and both Bully and San Andreas are all-time greats. I'd love to see a sequel to Bully someday.
I've seen Burnout Revenge mentioned a few times, and I would have to agree. That game was addictive, and crash mode is a feature that has yet to be matched by any contemporary racing games.