I had a lot of PS2 games, but didn't super duper enjoy a whole lot of the ones I had. I missed out on a lot of the best ones unfortunately. Trying to come up with some names, only things that spring to mind are Ico, Soul Calibur 3, and Metal Gear Solid 2

...Oh yeah. Champions of Norrath. So fun

Demon Stone was extremely good too

And I only played it on GameCube, but Beyond Good and Evil was available. And super awesome

Great topic for someone who was immediately banned