Dark Cloud 1 and 2, fun yet overlooked.
Ratchet and Clank series.
Jak and Daxter series. (Including Jak X, an immensely underrated racing game.)
God of War 1 and 2.
Armored Core (lots of them; IMO Armored Core 2 was the best.)
I would be doing some top-rated google searches if I were you, considering that the PS2's library is so massive. I own at least quadruple the games I listed above, but they are definitely the ones I enjoyed the most/got the most value out of.