Like the title says what is the first game(s) you ever had for your Xbox? For me it was Halo, PGR and DOA3. Uncle I live with bought those on launch day. 
 
(Note: You have to have owned an Xbox to post, obviously.)
   

Sega GT 2002/Jet Set Radio Future 
 
They came bundled in with my Xbox.

hard to say because it was my brothers xbox  :P

 Sega GT 2002/Jet Set Radio Future

I guess Ninja Gaiden Black, even though I downloaded it on my Xbox 360.  I never bought an original Xbox, but I always wanted one.

DOA3 and Cel Damage. I liked Cel Damage for a total of 10 seconds, but was absolutely in love with DOA and I played it constantly. 
 
PS It was a launch system and lasted me from 2001-2007. What a great console.

Fable
Crimson Skies
& Halo 2

If you are talking about the original Xbox that was entirely too long ago.  If you are talking about the 360 I believe I got Oblivion and the first 360 Burnout for Christmas with my 360.

Well wadda ya know I read the post wrong lol. I have no friggin Idea wht my first Original Xbox game was...  damn that was like 10 years ago man!

Fable and Halo 2.

Aparently It was Halo and PGR. had to look that one up. I remember taking the Metro home with my newly bought Xbox and trying to hide what it was (didn't fancy getting mugged) But completely forgot what games I had with it lol.

Sega GT 2002/Jet Set Radio Future.

Call of Duty 2. I never had and original Xbox. I was a PS2 kid but wanted a Xbox 360 in 05' because i didn't want to wait for for the PS3 and the 360 looked like my kinda system. I was and still am totally loving it. Call of Duty 2 was the best launch game of any system ever.

I have no idea what the very first one I got was, but one of the earliest I remember is Halo.
 
Around the same time, DoA3, Blood Wake and 4X4 EVO 2.
 
At least what I got from wiki that I think I have. But I do know Halo is one of the first I played. On a totally unrelated note, I saw Splashdown on the Wiki list and it totally reminded me of Wave Race 64. Loved that game (and the Twilight City or something map).

Halo and DOA3.  I still have both games,

 
Halo 2.

The first Halo game.

DOA3

I didn't own any consoles that generation...I did play a lot of backwards compatible games on my Xbox 360 back in 05/06 though. So, technically the first Xbox game I ever played was Splinter Cell: Chaos Theory. It still remains one of my favorites of all time, what a great game.

Halo for me. Was all i needed once i figured out you could use VPN software to play it online.

I never owned an Xbox, but Halo was the first original Xbox game I bought to play on my 360

Thanks to backwards compatibility I don't need to have owned an original Xbox to answer your question. My first and only original Xbox game was Halo 2.

My first ones were the ones that came packed with it; Star Wars: The Clone Wars and Tetris Worlds. And I bought Dead or Alive 3 when I bought my Xbox as well. Soon after that, I picked up Baldur's Gate: Dark Alliance.