ps1 - crash team racing

ps2 - cant remember

ps3 - Resistance 1

Genesis- Sonic

SNES- Mario world

64- Mario 64 and wave race

Gamecube- Luigis mansion and Rogue Squadron 

Wii- Twilight Princess

PS1- Crash 

PS2- FFX

ps3- RFOM 

Dreamcast- Sonic adventures 

360- ninja blade 

GB- Bomberman 

GBA- Circle of the moon

DS- Mario Kart 

PSP- FFT War of the lions

PC- Like I could possibly remember 

SuperNintendo: Goal, Super Mario World

GBA: Pokemon Blue

N64: Mario Kart, TloZ Oot

GB Advance: mario kart, Final fantasy tactics, Fire emblem

Gamecube: Wind waker, Metroid prime, final fantasy Crystal Chronicals

DS: mario kart, mario 64

Wii: TloZ TP, wiisports

PSP: Monster hunter 2G

I guess...

nes- super mario bros

Gameboy- Tetris

Gamegear-Sonic

snes- super mario world

genesis- sonic

N64- Ocarina of Time

PS1- FFVII

Gameboy Color- Pokemon Silver

Gameboy Advance sp- Zelda Minish cap

Dreamcast- Sonic Adventure

PS2- Ephemeral Phantasia

Gamecube- Pikmin

Wii- Twilight Princess

Ds- Zelda Phantom Hour Glass

psp- God of war Chains of Olympus

Xbox 360- Mass Effect

Well, I only remember starting with the SNES.

SNES: Super Mario Kart

PS1: Kagero (wish they would make a new game - different type of game that you dont see anymore)

PS2: GTA - Vice City (yes, I played Vice City before III lol)

PS3: Valkyria Chronicles.

NES: Super Mario Bros 1 and 3(special bundle)

Gameboy: Tetris and Spider-Man

Snes: Super Mario World

N64: Super Mario 64

GBC: Link's Awakening

GBA: Metroid Fusion

Gamecube: Eternal Darkness

DS: New Super Mario Bros

Wii: Wii Sports, Twilight Princess and Marvel Ultimate Alliance

XBOX360: Perfect Dark Zero

Playstation3: Batman Arkham Asylum

Atari 2600: Jungle Hunt

Commodore 64: Spy vs. Spy

Commodore 16/Plus 4: Death Race 16

Atari 7800: Donkey Kong

Nes: Teenage Mutant Ninja Turtles

Master System: Double Dragon

Gameboy: Super Mario Land 2

Snes: Street Fighter II: The World Warriors

Megadrive: Sonic

Atari Jaguar: Doom

PS1:  Lemmings 3D

N64: Goldeneye 007

Dreamcast: TrickStyle

Gameboy Advance: Castlevania: Circle of the Moon

GameCube: Burnout

Xbox 360: Perfect Dark Zero

Nintendo DS: Mario Karts

Wii: Wii Play

Oh wow, you're testing my memory for sure.  Only the first purchased game(s) not including pack-ins, here we go:

Atari 2600 - Defender.  I think Pac-man was the pack-in, but I was so young then I'm not sure.

NES - Rygar.

Genesis - Space Harrier II

Sega CD - ..... I honestly can't remember.  Wow.  Maybe Road Avenger ...

Saturn - Sega Rally

N64 - The Legend of Zelda: Ocarina of Time

Dreamcast - Sonic Adventure, NFL 2K, Soul Caliber (Bought all 3 at launch)

Playstation 2 - NFL 2K3

Xbox - Panzer Dragoon Orta, Jet Set Radio Future (if you haven't guessed, I was a Sega fan)

Gamecube - Super Mario Sunshine

Xbox 360 - NBA 2K6, Kameo

For the life of me I can't remember anything past this generation, but then again I only had PC, Sega Megadrive and PS1.

First game I got X360 with was COD4: MW, still to this day, one of my best purchases x)

NES & Mega Drive: Don't remember. My brother bought em'.

Game Boy: Super Mario Land. (I think)

SNES: Bought by my brother, but the first game he bought was Super Mario World.

Playstation: Same as above, just swap Super Mario World with Crash Bandicoot.

Nintendo 64: Super Mario 64, The Legend of Zelda: Ocarina of Time, Banjo-Kazooie, FIFA 99, GoldenEye 007.

Dreamcast: Sonic Adventure.

Playstation 2: Jak & Daxter: The Precursor Legacy.

Gamecube: Super Smash Bros. Melee.

Game Boy Advance: Metroid Fusion.

Nintendo DS: New Super Mario Bros.

Wii: The Legend of Zelda: Twilight Princess, Wii Sports.

Xbox 360: Dead Rising.

PSP: Ratchet & Clank: Size Matters.

Playstation 3: LittleBigPlanet, Uncharted: Drake's Fortune.