[Leesa]

Mortal Kombat is good, the upcoming one seems awesome. MK vs DC wasn't the best I hear, but I'm sure its fine. It's also the first T game for MK so the gore is muuucchh less.

If you like final fantasy get FF13, but it's long as hell and very repetitive. Graphics and cutscenes are spectacular, but you have like 5 long cutscenes probably every hour or so. (I personally hated it and returned it after like 5 hours of gameplay >_>)

Uncharted 2 is awesome and it features differently staged co-op modes as well as online. I suggest playing Uncharted 1 first though. Though if someone doesn't know English very well it'll be a challenge knowing what to do, as it is very story driven.

Ratchet&Clank series is cute and creative, as well as simple :P The humor thats targeted to younger audiences can get a little annoying but, it's a great series. Pretty sure none of them have online/co-op tho.

There are more games, just gotta look around.

Edit: Little Big Planet would be great for everyone, and racing games as well. Burnout Paradise, Need for Speed: Shift, Need for Speed: Hot Pursuit, and Mod Nation Racers are all great.