....your consoles? Please don't write bundled games. Nintendo DS: Nintendogs. PSP: NFS Underground Rivals. PS3: Resistance. 360: Halo 3. Wii: LoZ Twilight Princess.

GB: a pokemon game
PS1: Crash Bandicoot 3
PS2: SSX
PS3: Motorstorm (I also got another 2 games on launch)
PSP: Ridge Racers

On consoles I haven't owned these are the first I have played:
Xbox: cant remember
360: Call of Duty 3
Wii: Wii sports (only 1)
NDS: Final Fantasy XII: Revenent Wings

Megadrive II: Think it was Sonic
PS1: Crash Bandicoot, Abe's Odyssey
PS2: SSX
PSP: Ridge Racer
PS3: Resistance & Motorstorm

Atari 2600 : Pitfall (full of win)

NES : Zelda (full of win)

Snes : Mario (full of win as well)

Wii : Zelda (see one through three)

360 : Gears of War (see four)

Nintendo ds: NSMB
wii: excite truck

ps3 - def jam icon
wii - smg

NES: Super Mario Bros 3
Atari: I believe it was joust
SNES: LoZ LttP
Gen: Sonic 1
Sega CD: Sonic CD
N64: Mario 64
PS1: WCW Thunder
GC: Luigis Mansion
PS2: FFX
Wii: LoZ:TP
360: Oblivion
GB: TMNT (I think it was like Nightmare something I dunno but it was awesome)
GBC: Pokemon
GBA: Mario Kart I believe (can't remember)
DS: Mario 64
PSP: Crisis Core
Game Gear: Sonic

PSone : Alien Trilogy
PS2 : Jak & Daxter
PSP: Wipeout Pure
DS : NSMB
NES : Mario Bros ( and it wasnt bundled )
SNES : have no idea
Atari 2600 : same
GB : Tetris
GC : have no idea ( Though I think it was Rouge Squadron )
GBA : same ( it could have been one of the GBA Crash games ...)
N-gage : Tomb Raider ( :P )

Two or more games means I purchased two or more games with my system purchase, naturally. 

NES: Super Mario Bros. 2
SNES: Krusty's Super Fun House
Genesis: Terminator 2: The Arcade Game
Gameboy: Super Mario Land + Gremlins 2
Gameboy Advance: F-Zero Advance + Tony Hawks Pro Skater 2
Virtual Boy: Wario Land
Jaguar: Aliens vs. Predator + Trevor McFur in the Crescent Galaxy
PSOne: Mortal Kombat Mythologies + Crash Bandicoot 2
N64: GoldenEye007, Super Mario 64 + WCW vs. NWO: World Tour
Dreamcast: Sonic Adventure + Soul Calibur
Gamecube: Luigi's Mansion + Super Smash Bros. Melee
PS2: Onimusha Warlords
Nintendo DS: Super Mario 64 DS
Xbox 360: Gears of War + Dead or Alive 4
Wii: Super Mario Galaxy + Legend of Zelda: Twilight Princess
Sony PSP: Jeanne D'Arc, Disgaea, Final Fantasy Tactics, Silent Hill Origins, Crush + Syphon Filter: Dark Mirror(I really went all out with my PSP buy. I still haven't unwrapped Jeanne D'Arc from the shrink wrap.)

Genesis: Sonic the Hedgehog 2 (Amazing Game, in my top 5 to this day)
N64: Diddy Kong Racing (My first 3D game, I was in shock. Tiptup was my racer of choice. :P)
GCN: Super Smash Bros. Melee (Played it and as Falco until its dying day [Brawl])
Wii: The Legend of Zelda: Twilight Princess (Blown away, another masterpiece)

GBC: Super Mario Land 2 (A great platformer. Good times with this one)
GBA: Super Mario Bros. 2 (A Mario game that wasn't exactly Mario... for obvious reasons)
DS: Super Mario 64 DS (A nice little remake with some cool extras. Control took some getting used to)