I'm currently about half-way through Earth Defense Force 2017, and I can't recommend it enough. It's an almost stupidly simplistic third-person shooter, but it's strangely addictive, and the enemies are larger than life. It's extremely fun in co-op, too.

Also: The Orange Box is a must-have, if you don't already have it for PC.

As for XBLA, my favorite download is Pac-Man Championship Edition, which is great to pick up and go a few rounds with for 10-15 minutes on a whim. Also remember to grab Aegis Wing, since it's free.

/\ QFT - I have it and really, it's an awesome game. With the controllers, that and Orange Box are the best values in gaming for 2007. 

1- Mass Effect
2- Gears of War
3- Bioshoke
4- Oblivion
5- Dead Rising

Great Games

The 360 games I personally feel are must haves are:

1 - Bioshock
2 - Dead Rising
3 - Halo 3
4 - The Orange Box
5 - Mass Effect
6 - Elder Scrolls IV: Oblivion

Possibly Assassin's Creed. I have it, but have not been able to play it for more than 10 minutes yet.

For third person shooters, Gears of War

First person shooter, get Call of Duty 4

Party game, get Guitar Hero 3

RPG, get Mass Effect

Action Adventure, get Dead Rising

There are some great games out there already but don't be too hasty, there are some great games out this year such as Alan Wake, Too Human and Fable 2. No doubt plenty more games yet to be announced as well! Enjoy your 360 fun.

Viva Pinata looks awesome.

My list is basically the same as Hawk's- just in a different order.

Also, look at older games like Condemned, Burnout Revenge, and Kameo. Lots of fun to be had for $15-$20. If you're like me, you never know what you want to play, so diversity is a must.

Which I have played, and know they're good:

Oblivion
Call of Duty 4 (and CoD2 also, it's very cheap now and it's a good game)
Guitar Hero 2 & 3
Forza Motorsport 2
Burnout Revenge (Burnout Paradise should be on stores soon though...)
Virtua Fighter 5
Dead or Alive 4
Dead Rising
.
.
.
And then there's many games that I know are good, and I'm planning to buy. Like:

Orange Box
Rock Band
Mass Effect
Assassin's Creed and so on...

And there's older games (Classic games), which you an get in good price:

GRAW
PGR3
Condemned
Saints Row
Kameo etc..

Xbox 360 really has alot of good games, it shouldn't be hard to find something you like. :)

nice simple list RSeagle... niceeee