My girlfriend has a PS2, but the price is low enough for me to go and buy one. I already have a couple of games which i play when i'm at her place, but these lists of you guys was just what i needed since i forgot about half of everything mentioned above.
These games have already been mentioned, but they deserve more emphasis.
Rez
Not a real game, but an excellent experience like no other.
Castlevania Lament of Innonce
Take the endless hallways for granted, since the animations, the story, the bossfights, the characters, the battle-system and the music are all top-notch. Only buy Curse of Darkness if you're a big Castlevania like me, otherwise you'd stop playing the game after two hours out of boredom.
Devil May Cry series
Two awesome games, and a black sheep. Stay away from DMC2, since it is dreadful game. Part 1 and 3 are among the best i've ever played.
I've got more, but the rest isn't as good as already mentiond.