Just got a PS2! What games do you recommend I should buy?

This is what I want to buy so far:

• Ico
• Shadow of the Colossus
• SSX
• Final Fantasy X
• The Red Star
• Valkyrie Profile 2: Silmeria
• Fatal Frame
• Katamari Damacy
• Twisted Metal Black
• We Love Katamari
• Black
• Silent Hill 2, 3
• Burnout
• Devil May Cry
• God Of War
• Ratchet & Clank (all of them!)

Anybody got any recommendations? I'm cool with games that are lesser know or had flaws, as long as they had unique or interesting elements.

EDIT: Thank you all for all the great recommendations, especially the obscure titles and JRPGs. Does anybody have any recommendations for puzzle games or offbeat games (offbeat = same vein as Vib-Ribbon or Chu Chu Rocket?)