I got my 360 Christmas 2005 and got Call of Duty 2 and Most Wanted for it. I remember right around the time the 360 launched there were kiosks at Best Buy that all had CoD 2 on them which is what sold me on the game. Never tried Kameo or Perfect Dark surprisingly.

Kameo, but I didn't actually play it, so I'd say Guitar Hero 2.

My first game was Dead Rising.

Halo 3. Still one of my favourites!

Sneak King.

Kameo was my first game, I got my 360 a month before release date. So I couldn't even buy another game and there was no Multiplayer or Co-op mode when Kameo was released. Then it was Need for Speed: Most Wanted.

When I first got my 360 on launch day, I got PGR3, Kameo and NBA 2K6.

Oblivion and Perfect Dark Zero, played Oblivion first. Got Kameo maybe a week later. Hey, thanks for reminding me of Kameo, it was a pretty good game.

Perfect Dark Zero, came with the 360 VIP pack that was sent out before the 360 launched here in New Zealand .

Lost Planet and Halo 3, i was a little late to the party.

Call of Duty 2 on Veteran! Brilliant start for my 360 :)

Gears of War!

Dead Rising, i think?

pgr3

For me it was NCAA Football 2008.

Mine was Kameo.  It was released a few days before the system and I bought it then waited for launch night.  I also picked up PDZ and Call of Duty 2 

Got my 360 in summer 2007. The first two games I bought for it were F.E.A.R. and Far Cry Instincts: Predator. I still own both of those, too.

I rented Call of Duty 2, Condemned and Project Gotham Racing 3 the first night I bought my 360. :)

Halo 3 , I was rocking my PS2 up until H3's launch.

The Darkness. I loved that game too bad the multiplayer was shit.

Dead Rising

Kameo and Perfect Dark Zero. 

*sigh*

I am not proud.

" Gears of War for me. "

Gears of War.  My friend made an offhand remark about wanting to play it so I bought the system and game so we could co-op.
 
I remember we went on the day it was being midnight released to buy God of War or something completely unrelated. We laughed, "Who would stand in line to buy something called Gears of War?" 
Three months later or so, microsoft had the last guffaw.

DOA 4 & GTA 4.

Kameo, loved it at the time.

Halo 3

Gears?

Call of Duty 2 and Need for Speed: Most Wanted.
 
I was 100% sold on the 360 after that.
 
Prior to playing those games, I was berating my brother for wasting money on a launch console he didn't need, and after playing them, I ate my words and have been loving the 360 ever since.

I got my 360 a couple weeks after Bioshock came out, so I got that. Great way to start off the new generation. :)

TES IV Oblivion.  Then GRAW, not for long though, eeugh.
 
Wish I had gotten either Perfect Dark Zero, Call of Duty 2, or Condemned: Criminal Origins instead of GRAW.

I had borrowed some games like Crackdown and stuff, but the first game I went out and bought was Bioshock.

I'd have to say Dead Rising popped my cherry.

Crackdown was my first 360 game
bought it the same day as my 360

Perfect Dark Zero which I enjoyed, but I got Oblivion a little while later and loved it.

cod2

I believe Ghost Recond Advanced Warfighter. Not the best choice I could have gotten...never really thought it was all that BAMF.

My first 360 game was Halo3, but lost planet, dead rising and crackdown were the first 360 experiences for me. Resistance and motorstorm were my first nextgen games.

I got Need for Speed Shift included with my 360, so yep, that!