ratchet and clank (all three), jak and daxter (all three), come to mind right off the bat
While I love the first 2 games in each of those series, the third games aren't even out yet, so I don't see how you could recommend them.
I'll second ICO.... the most under-rated game ever on PS2.
Gran Turismo 3
Eye Toy is cool for parties/groups... not quite a game though, more of a bunch of minigames
Sly Cooper and the Thievius Raccoonus
Klonoa 2
Final Fantasy X and X-2 if you're into RPGs
Frequency/Amplitude (not sure if they are exclusive)
Dark Cloud 2
I can't think of any more right now, but there are a lot of great PS2 only games.