So I just got a PlayStation 2...

[ReservoirAngel]

STOP! don't get any of those 3 games! ico and shadow of the colossus are being released HD when last guardian comes out

I don't have a PS3 though, so getting them on my PS2 is the only way I can play such awesomeness.

silent hill 2 is terrible.

After praise for this game from 99% of the people who can render opinions on it, I am somewhat forced to disregard this viewpoint. It's pretty much you against the world on this right now.

 

[Dale Cooper]

We Love Katamari
Silent Hill 2 and 3
Fatal Frame (any)
Resident Evil 4
Psychonauts
Marvel Ultimate Alliance
Eco
Shadow of the CColossus

 

[Rhymenoceros]

The ratchet and Clank series was definitely my favourite of the PS2 era.

Although ionically I got in from town 10 minutes ago after just selling all my PS2 games to cex

 

[ChupathingyX]

Just buy every game made by Naughty Dog and Insomniac Games on the PS2.

 

[Seabear]

Crash 3 and CTR? I know they were PS1 but my god, fantastic good fun. While I'm on PS1- Jade Cocoon.

 

[linkblade91]

Ratchet & Clank - 1, 2: Going Commando, 3: Up Your Arsenal
Kingdom Hearts- 1, 2
Grand Theft Autos - III, Vice City, and San Andreas
Persona 4
God of War - 1, 2
Okami

While I cannot attest to Persona 4, having never played it myself, I'd second the notion of picking up the others. Especially Ratchet&Clank; they are undoubtedly my favorite game series. Shout-out to Okami, Kingdom Hearts, and God of War as well.

To contribute something of my own (rather than merely flapping my gums in a long-winded "This!" post), I'd also suggest the Jak&Daxter and Sly Cooper series(s?) as well. The "Playstation Move Heroes" PS3 game combines R&C, J&D, and SC into a match made in heaven...if it weren't exclusive to the Playstation Move, that I have no other reason to want (grumbles to himself...).

And if you like those three, the developers did branch into some new IPs on the PS3, namely an alternate-history-with-aliens FPS (Insomnaic; R&C --> Resistance), an Indiana Jones-style adventure (Naughty Dog; J&D --> Uncharted), and an electricity-based superhero sandbox (Sucker Punch; SC --> Infamous). Just something to keep in mind for the future

Edit: Now that I think harder on the subject, I can think of so many great PS2 games: Burnout 3, FFX, the Katamari series (if you can handle zany Japanese-weirdness), the Prince of Persia games, Star Wars Battlefront II (if you had a friend who'd play with you); there's too many to count! lol