God of War Saga,
Skyrim,
Oblivion,
Katmari Forever,
Soul Calibur IV,
Soul Calibur V,
The Orange Box,
Rainbow 6 Vegas 2,
Red Dead Redemption GOTY,
Mass Effect Trilogy,
Medal of Honor,
Portal 2,
Final Fantasy XIII,
Final Fantasy XIII-2,
Call of Duty 4: Modern Warfare,
Call of Duty: Modern Warfare 2,
Call of Duty: Modern Warfare 3,
Naughty Bear (for the novelty of owning it, it's ridiculously cheap),
SOCOM 4,
Little Big Planet (with friends),
Little Big Planet 2 (same idea, include friends),
Resistance: Fall of Man,
Resistance 2,
Resistance 3,
Borderlands GOTY,
Dead Island,
Ace Combat: Assault Horizon,
Deus Ex,
Call of Duty Black Ops,
Call of Duty Black Ops II,
Fallout 3 GOTY,
Fallout: New Vegas Ultimate Edition,
Twisted Metal,
inFAMOUS,
inFAMOUS 2,
Batman: Arkham Asylum,
Batman: Arkham City,
Red Faction: Guerilla,
Red Factio: Armageddon,
Resident Evil Anthology,
Killzone,
Killzone 2,
Killzone 3,
Ratchet and Clank Collection,
Ico/Shadow of the Colossus Collection,
Bioshock,
Bioshock 2,
Dead Space,
Dead Space 2,
Battlefield: Bad Company,
Battlefield: Bad Company 2,
Battlefield: Bad Company 3 Premium Edition,
Haze,
Crysis 2,
Sonic's Genesis Collection,
Just Cause 2,
And lastly,
Super Street Fighter IV.
That's my personal library at least.
Edit: Forgot to include Borderlands 2 and Playstation Allstars Battle Royale.
Edit: Edit: Edit: also missed Demon's Souls.
Suggestions as additions (which I'll buy once my funds allow it)
Gran Turismo 5,
XCOM: Enemy Unknown,
Heavy Rain,
LA Noir,
And Heavenly Blade.