What's your favourite online game for the PS3. And yes it can be multiplatform for example Call of Duty.
Here are some good suggestion:
Warhawk
Call of Duty Black Ops
Call of Duty Modern Warfare 2
Call of duty Modern Warfare
Uncharted 2
Killzone 3
Killzone 2
Little Big Planet 2
Little Big Planet
Grand Theft Auto 4
Metal Gear Solid 4
Gran Turismo 5
You can pick any game as long as it's on PS3