Being a Nintendo fan, the only PS console I owned before is the PSP (aka my Monster Hunter machine). I did already have some PS2 games in my mind to get (Xenosaga, Star Ocean, ICO), but it's always nice to have other opinions!
EDIT: Thank you so much everyone! I never expected that many replies XD
After looking through the replies, here's what I got (after weeding out the games that I am not that interested):
Xenosaga I/II/III
Xenogears
Star Ocean
Metal Gears series
Dark Cloud 2
Rogue Galaxy
Shadow of the Colossus
ICO
Bully
Persona 3
Persona 4
Disgaea 1/2
Resident Evil 4
Final Fantasy X/XII
Devil May Cry 1/3
Onimusha series
God of War I/II
Silent Hill 2
Haunting Ground
Rule of Rose
Forbidden Siren
Forbidden Siren 2
Kessen 1-3
Timesplitters 1-3
Kingdom Hearts 1 and 2
Kingdom Hearts: Chain of Memories
Jak and Daxter series
Sly Cooper series
Gran Turismo 3/4
Ace Combat 4/5/0
Katamari Damacy
Dragon Quest VIII
Shadow Hearts Covenant
Prince of Persia
Suikoden 3
Megaman X Collection
Onimusha
Wild Arms
Mana series
Ar tonelico
Grandia 2 & 3
Castlevania: Symphony of the Night
God Hand
Yakuza 1&2
the SMTs
Viewtiful Joe
Legacy of Kain series
I might get some of them for different systems instead of the PS2 version, but holy shit that's impressive... Being interested in most genres doesn't really help either.













