Super Nintendo: Super Mario's World

PS1: Power Rangers Time Force

Dreamcast: Sonic Adventure

PS2: ATV Offroad Fury 2

Xbox: GTA: San Andreas

Wii: Super Smash Bros

PS3: Fight Night Round 6

PSP: King Kong

PS Vita: GTA Chinatown Wars

First game on PS4 will most likely be Call of Duty Ghosts.

First Xbox game will probaly be Halo next year.

Let's see....

SNES: I don't remember which game I got first. Too young. Possibly Super Mario All Stars or DKC.
N64: Pokemon Stadium 2
GC: Super Smash Bros Melee, Mario Party 4
Wii: Twilight Princess
Game Boy: Pokemon Yellow
GBA: Pokemon Sapphire
DS: Mario Kart DS
3DS: Super Mario 3D Land
PS1: Final Fantasy VII
PS2: Final Fantasy X
PS3: inFAMOUS
PSP: Star Ocean First Departure
PSVita: Uncharted Golden Abyss, WipEout 2048, Hot Shots Golf International

Systems for the future:
Wii U: Zelda Wii U
PS4: I'm considering getting one when Second Son comes out, since the first one was my first PS3 game.

NES: Super Mario Bros and Super Mario Bros 3
SNES: Super Mario World
N64: Super Mario 64
GCN: Eternal Darkness, Resident Evil, Resident Evil 0
Wii: Wii Sports, The Legend of Zelda Twilight Princess
WiiU: New Super Mario Bros U, Assassin's Creed 3. ZombiU, Darksiders 2, Call of Duty Black Ops 2
Ps3: Batman Arkham Asylum

Game Boy: Tetris, The Amazing Spider-Man
Game Boy Color: The Legend of Zelda Link's Awakening DX
Game Boy Advance: Metroid Fusion
Nintendo DS: New Super Mario Bros
Nintendo 3DS: Super Street Fighter 4
Sony PSP: Assassin's Creed Bloodlines, Dracula X Chronicles

NES: Super Mario Bros.

SNES: Earthbound

N64: LoZ: Ocarina of Time

Gamecube: Super Smash Bros. Melee

Wii: Wii Sports

Gameboy: Tetris

Gameboy Advance: Pokemon Leaf Green

DS: Pokemon Diamond

3DS: LoZ: Ocarina of Time remake

Xbox: Halo

Xbox 360: Saints Row

PS2: Mortal Kombat Deadly Alliance

PS3: Resistance: Fall of Man

Dreamcast: Ms. Pacman Maze Madness

PC:
-can't really remember, but I'll say Chip's Challenge

SEGA Genesis:
-Sonic 1 or 2 (can't remember which I got first)

Game Gear:
-Sonic Triple Trouble

Game Boy Color:
-Pokemon Blue

SEGA Dreamcast:
-Sonic Adventure

Playstation 2:
-ATV Offroady Fury 2

Xbox:
-Halo: Combat Evolved

Xbox 360:
-Mass Effect

I expect to get an Xbox One early next year when Project Spark is finalized.

NES
smb/duckhunt & tloz

SNES
smw & f-zero & pilotwiings

N64
sm64 & pilotwings

Dreamcast
sonic adventure & soulcalibur & mk gold & hydrothunder

XBOX
halo ce & munch's oddysee & doa 3

Gamecube
luigi's mansion

Playstation 2
galactic wrestling & rygar

XBOX 360
tes iv oblivion

Wii
metroid prime iii

Playstation 3
lbp

PSPGO
gta stories

PC
skyrim

3DS
pilotwings resort

PSVITA
mortal kombat 9

Wii U
nsmbu & zombiu

Hmm that's going to take some thought

First console only had pong and different variations built in.
Next was Nes and I got Batman
Snes Super Mario world
N64 Zelda
PS Metal Gear
PC Civ
PS2 Summoner but I had to take it back the day I got it because it was faulty. Didn't get another one
My GF had a Gamecube and I got Zelda for it
Other than that its been PC ever since except this gen I got a Wii U. Zombi U was my first game other than Nintendo lan

Love the idea behind this thread! Let's see what I can remember...

PS3 - Assassin's Creed (horrible start to the generation for me, should have just waited for Uncharted which was my second game if I'm not mistaken)

PS2 - Grant Theft Auto III (not 100% sure though, could also have been Final Fantasy X)

PS1 - Silent Hill (bought the game before I bought the console and it was so worth it)

PSP - Grand Theft Auto: Liberty City Stories

Gamecube - Super Smash Bros Brawl (only because it came with the console when I bought it, not really into this series; the first game I got because I really wanted it was Luigi's Mansion)

N64 - all 7 games I have for it came with the console when it was given to me

DS - Super Mario 64 (or Warioware, can't remember now)

Gameboy Advance - Castlevania: Circle of the Moon

Gameboy - Tetris (came with the handheld)

Dreamcast - Sonic Adventure

Saturn - Daytona USA (came with the console)

Mega Drive - Sonic the Hedgehog (came with the console I believe)

Edit: Planning on getting a PS4 only.

NES - Super Mario Bros

SNES - Super Mario World

Gameboy - Zelda: Link's Awakening

Gamegear - Mega Man

N64 - Super Mario 64

Playstation - Megaman 8

Neo Geo Pocket Color - King of Fighters R2

Playstation 2 - Armored Core 2

Gamecube - Star Fox Adventure

PSP - Twisted Metal: Head On

Playstation 3 - Oblivion

Wii - Monster Hunter Tri

Planning on getting a PS4, no clue what my first game will be.

gameboy: mario
gameboy color: pokemon silver
nes: balloon fight
snes: mario kart
play station: tekken 3
gb advance: super streetfighter
nin ds: pokemon diamond
ps2: ff x
wii: sports
3ds: kid icarus