Halo 3 for sure
Try to pick up Geometry wars, which is an xbox arcade game. Other than that, this is what I suggest.

-Gears of War
-Rainbow Six: Vegas
-Call of duty games
-Orange Box
-TES: Oblivion
-Condemned: Criminal Origins
-Eternal Sonata
-Perfect Dark Zero
-Bioshock
-F.E.A.R.

You did not mention your tastes and if you were a big PC gamer or not, so I just gave you a short list of what I recommend off the top of my head. There are a lot of missing I am sure, but whatever.

CoD3 is shit! Seriously, don't get it unless you plan on playing multiplayer. The singleplayer is awful (and I LOVED both CoD1 and 2). So yeah, this comes from a CoD fan. The 3rd one has awful singleplayer and decent multiplayer (a watered down BF42 kinda, just more CoD'ish).

I suggest NOT getting NFS: Carbon... I got it and it sucks. if you MUST get a NFS game though I go for Most Wanted (since it's older its probably cheaper) or even just wait for the next NFS to come out. I'll elaborate a tiny bit: The "team" based racing in Carbon just doesn't work well, it is actually kind of annoying, and the police chases in Most Wanted is pretty fun. The ones in carbon feel some what dull.

Anyway, I have not tried it yet, but I heard PGR4 is pretty awesome.
and Bioshock if you want a good single player FPS experience.

Rainbow Six: Vegas is a excellent choice for a Tactical FPS, I mean I don't even like many tactical FPS's but this one just kicks utter ass. (I personally think its more fun then Gears of War) The single player can be on the short side if you choose 'normal' as the difficulty for your first run., So I recommend realistic, it will lengthen you're experience if you decide to play that on you're first run.

I second the DO NOT BUY PDZ. It felt exceptionally generic and dull in the single player. although the multiplayer was still generic, it wasn't as dull.

if you're going to get any CoD wait for 4.

If you've never played nor owned Worms for PC (Like I haven't) then I Recommend Worms the Arcade game.

If you like multiplayer platforming shooters I recommend Small Arms, just don't expect to find anyone online playing it, stick to 4 player, 4 controllers offline.

The only reason I'm not recommending the orange box is because I myself have yet to play Portal and TF2, and I really think those game would probably be wiser bought for PC. In fact I don't plan on buying the Orange box at all, I'm going to buy the valve complete pack through steam once I get the cash. (Hopefully soon, but unlikely to be soon.)

Oh and I urge you to reconsider Halo 3. I did not personally like Halo 2 all that much. but 3 seems to reclaim some of the awesomeness that the original had. If you liked the original, and like multiplayer it is worth the $60.

two games you just listed aren't fps

Or get a 360 for every other game that isn't a fps

you know, like mass effect, ninja gaiden 2, table tennis, crackdown, gta4, guitar hero 3, assassin's creed and lots of other shit.

oh and about 90% of the games on xbla are really fucking good.

oh well if you are looking for a list then:

Beautiful Katamari (better than Me & My Katamari and Katamari Damacy, but not as good as We <3 Katamari)
Ninja Gaiden 2
Mass Effect
Table Tennis
Assassin's Creed
Devil May Cry 4
Super Street Fighter II Turbo HD Remix
Puzzle Quest
Blue Dragon
Enchanted Arms (yeah it's kinda ridiculous at first but beyond its stupidity is a really really fun to play RPG)
Eternal Sonata
Ace Combat 6
Marvel Ultimated Alliance: Gold Edition (only version to have the 8 extra heroes)
Too Human
Alone in the Dark 5
Infinite Undiscovery


and yeah I could go on and on and I know not all of those are just for 360 but it's STILL AVAILABLE for it so it's not like it's not a valid point.

so yeah, the 360 is not just fps and brutal action games and shit.