Open World Game Suggestions

The Saboteur

Sleeping dogs

Just cause 2

Infamous 1 and 2

Infamous, Fallout 3, The Saboteur, and possibly Yakuza 4 (really fun game but might not be what you're looking for).

far cry 3

tomb raider

On the PS2 I really loved Drakan:  The Ancient Gates.  Open-world action/RPG (pretty light on the RPG aspects, just buying weapons and spells), with a beautiful world and you even get to fly around on a dragon. 

On the PS3 my favorite open world games are Skyrim, Fallout 3, The Saboteur and Nier.

I highly recommend Sleeping Dogs. It's cheap, great visuals, great story as mentioned above and also the combat is extremely fun

The Assassins Creed games, start with 2. (Don't know how no one's mentioned these yet)

Sleeping Dogs, GTA in Hong Kong, amazing game. 

The Saboteur

Skyrim

Oblivion

Batman Arkham City is open although on a much smaller scale. Arkham Asylum as well.

Far Cry 3

Far Cry 2 although it sucks. 

Just Cause 2 which people seem to love but I thought it was pretty heh.

Fallout 3

Dragons Dogma

The Amazing Spiderman

Few RPG's and/or other games with elements of an open world (Sections of smaller open worlds)

Deus Ex: HR, Mass Effect series, Dragon age Origins, Dark Souls, Dishonored. 

Sandbox wise, you can't do better than Saints 2 imo (3 was bleh), though I hear Just Cause 2 is pretty great as well.

Open world period? Fallout: New Vegas is one of my favorite games of all time, as long as you don't mind it being an RPG. I also really, really enjoyed Prototype 2, pure fun.

Assassins Creed 2

Red Dead Redemption

InFamous 1 and 2

GTA4