The first game you owned for each of your consoles

[Zimbacca]

Let's see all that I can remember...

Atari - too young to remember

NES -Mario/Duckhunt

Genesis - Sonic

SNES - Legend of Zelda: Link to the Past

PSX - FF7

PS2 - Dark Cloud

Gamecube - Animal Crossing

Xbox - Halo

Game boy - Tetris

Game boy Advanced - Lufia

[m3talst0rm]

Atari 7800 (Sadly, I no longer have this system, but I will have you back my beautiful Prosystem!): When I got this system my mother bought it for my brother and myself (yeah, he got it ).  We found it, along with a bunch of games, at Odd Lots (Big Lots) for real cheap.  Anyway my favorite of this first bunch was Food Fight.

NES: Obviously Mario/Duckhunt.  

SNES: Super Mario World.

N64: (1st time around) Mario 64 (2nd) Zelda: Ocarina of Time

Virtual Boy: Mario Tennis and Red Alarm

Gameboy Advance SP: Street Fighter Alpha

Game Cube: Super Smash Bros.

Sega Genesis: Road Rash II

Colecovison: donkey kong

My Gamegear, Odyssey 2, Atari 2600, and Atari 5200 all came with a bunch of games so I really dont have just a "first" for them.  
Here are my favorites of the first batch for those consoles.

Gamegear: Shinobi
O2: KC Munchkin
VCS: Taz
5200: Um, still no rf adaptor so I cant play.  Oh, I cant wait to spin that trackball!

[shaggy]

Hard to remember but let me think:

NES:  Mario/Duckhunt pack-in.  First bought game, can't remember.
SNES:  I think Mario World was packed in. First bought game was Super Stree Fighter II I believe
N64: Mario 64
Sega CD: Sewer Shark or Dracula Unleashes I think
More to come later when I remember.