It all depends on what types of games you like to play.
I play mostly first person shooters, but also own some really great single player titles.
As for online play,
Gears of War 2 kicks ass. I've been playing a lot of that lately.
I recently picked up
Mortal Kombat vs. DC Universe and it's fantastic.
Of course, if you're into WW2 shooters like I am,
Call of Duty 3 is a must-own.
I hated Call of Duty 4 and Call of Duty: World At War is just ok.
You'll love to play
GTA4 on Live. It has some really intense online games. I own GTA4 but haven't played it in quite awhile. I may have to pop that one in soon and play it.
Some must-own single player games are
Oblivion,
Fallout 3 and
Dead Space.
Dead Space was a total surprise to me. It's scary as hell and the graphics are some of the best I've ever seen in a game.
I also own several games for Xbox Live Arcade.
Bionic Commando Rearmed is really good as is
Geometry Wars Evolved 2.
Live Arcade also has several good card games. A must-own is
Uno. I can't even begin to count how many hours I've spent on that game. I also have
Hardwood Spades and
Gin Rummy. Both of those are only 400 Microsoft points each. ($5)
If you do get Live, add me to your friends list. My gamertag is ASHTHECAT3.
Spelled just like that in all caps.
You can view all my games
HERE