Here's my list:
-Any Bemani game (DDR, Beatmania, PUI, etc)
-Castlevania: Lament of Innocence
-Final Fantasy VII: Dirge of Cerberus
-Final Fantasy X and XII
-God of War
-Kingdom Hearts I and II
-Soul Caliber III
-Timesplitters: Future Perfect
-Wild Arms: Alter Code F
Honestly, the list could go on, but these were all games I couldn't put down, even after I beat them, especially Dirge and Future Perfect. The PS2 was a very impressive system, and my personal favorite from the last console generation.