I never owned a PS2 when they were still being manufactured and sold. I still do not own a PS2. However, there are some games I actually liked that released on PS2 (I did not list games that were better on other platforms, for example, Silent Hill 2 Enhanced Edition on PC is still the best way to play SH2):

Metal Gear Solid 3

Kuon

King’s Field 4

CyGirls (I liked Disk 1 more than Disk 2)

Drakengard 1 and 2

Shadow of the Colossus

Ghost in the Shell Stand Alone Complex

Extermination

Lifeline

Ico