Dude you are really,really really late to the party there are a lots and lots of must haves on the ps2 that is too hard to name them all but get:
GOW 2
shadow of the colossus
kingdom hearts I,II
FF X,XII
Grand Theft Auto III,Vice City,San Andreas
Dragon Quest VIII: Journey of the Cursed King
Guitar hero I,II
Those are only a few of a lot of awesone ps2 games ,btw mod your ps2 .