I have a Nintendo Wii too (I am not a fanboy), mainly for my son and wife, but I already played everything I wanted to play on that machine. Last Sunday they gave me as a father's day gift  a Jasper 2009 Xbox 360, mostly for me. I didn´t expected that, so I almost cannot believe it. I bought LEGO BATMAN for my son and Need for Speed Undercover for my wife. The rest of the games are for me. I think it is a pretty decent starter collection, but I was just wondering, is there an amazing game outthere I might have overlooked?

I like all the genres, excepting FPS, which must be awesome for me to play it

Here's my list:

Star Wars the Force Unleashec

GTA IV

Lego Batman

Street fighter IV

Oblivion

Mass Effect

NBA 2K9

Tales of Vesperia

Call of Duty 4 Modern Warfare

Gears of War

Gears of War 2

Civilization Revolution

Devil May Cry 4

Forza Motorsport 2

Lost Odyssey

Hawx

Need for Speed Undercover

Fable II

(Bioshock and Resident Evil 5 I can borrow from my brother)

Well, what do you think? Is there another game I should buy?

PS: I don't play online, so please recommend me games not strongly based on online multiplayer. Offline multiplayer, in the other hand, I will appreciate.

Viva Pinata, and banjo kazooie N&B

I think Halo 3 has 4 player splitscreen, so you may be interested in that.

@c03n3njo
yeah it does

excellent start, I'm assuming you don't have a ps3, as your op just says you have a wii as well. so my list of other game you might like (excluding FPS)

Halo Wars
condemned 1 and 2 (dirt cheap now, underapreciated games)
Oblivion
Fallout
prototype
Assassins creed
Dead Rising

For the Family
Scene it
Lips

Too bad you can't go on line because there are many good games to be have on Live. Just don't let your wife discover Peggles because you might not get your console back.

I recommend you purchase Dead Space. Dead Space is an exceptional game. 

Give Dead Rising a try. There's a free demo available on XBL.

I will go online eventually, but not this year...

Yes, I thought about that one. I might wait for the Wii version. Or maybe not. I do prefer Third Person Shooters over the FPS