God of War, and God of War 2.

Okami

Ratchet and Clank stuff

Shadow of the Colossus.

And 100 more :p

 I can't believe I forgot to mention God of War!

It is my user-name after all.....

@masschamber I was talking about fighters but I like beat em ups too.

Recommended so far:
Gran Turismo 3 & 4
Tekken 4 & 5
Soul Calibur 2 & 3
Godhand
Budokai Tenkaichi 2
Virtua Fighter 4
Mortal Kombat
WWE games
Burnout 2, 3 & 4
Need For Speed
Shadow of the Colossus
Okami
God of War 1 & 2
Socom
Capcom vs SNK 2
Ratchet and Clank
King of fighters 98
Fatal Fury Battle Archives
Street Fighter alpha anthology
SNK collection

why did you buy a ps2 and not a 360?

Shadow of the Collosus is a sandbox game, but pretty different to GTA and its clones.

okay then, also the second fatal fury battle archives is the good one, the one I was recommending, the first isn't nearly as good as the highlight is fatal fury special, which isn't nearly as good as Real Bout
and if you don't mind Japanese imports there is Garou Mark of the Wolves and Last Blade collection
plus regardless of taste you should give Katamai Damacy a try

@allergic Because it was £40! If I saw a 360 for £40 I'd buy that too.

If you ever try an RPG make sure Persona 3 FES is the one, full of win.

God of War, FF, Guilty Gears, GTA (triple pack).

Well here is a link to the top rated PS2 games.

MORE THAN 200 games have a rating of 82%!!!

Link: http://www.gamerankings.com/itemrankings/simpleratings.asp

You can also choose genres to filter through.