Monster rancher 4 (but not 3!)
Guilty Gear: X2 or XX accent core; avoid all others, especially isuka.
Those are the only reasons to own a ps2.
EDIT: I made a terrible mistake.
I forgot Katamari Damacy (and it's sequel) and Soul Calibur 3. (but beware of the memory card bug.)
that brings the total number of good games for the ps2 to a whopping
6.