N64: The Legend of Zelda: Ocarina of time
Playstation 2: God of War/Devil may Cry 3
PSP: Tekken Dark Resurection
PC: Mass Effect trilogy
Playstation 3: can´t decide too many high quality games (greatest gen so far)

DS: The Legend of Zelda: Phantom Hourglass

Wii: The Legend of Zelda: Twilight Princess

Sega Master system-Alex Kidd in miracle world,
Sega Mega drive (Genesis)- Sonic the hedgehog 1, Streets of rage 3, Road rash.
Sega Saturn- Sega Rally, Virtua fighter 2, Saturn Bomberman
Dreamcast-Shenmue, Metropolis street racer, R E Code Veronica
Gamecube- Wave race blue storm, Super mario sunshine, Zelda windwaker
Wii-Xenoblade chronicles, Super mario galaxy 1/2, Zelda Skyward sword.
DS-Nintendo touch golf, Mario v Donkey Kong, Metroid Prime Hunters.
3DS-Mario kart 7, Mario 3D land, Resident evil revelations
PS3-Batman Arkham city, Sonic generations, Rage (yes i enjoyed Rage)

Atari 2600: Cowboy

Commodore Plus4: Jack Attack

Commodore 64:  Creatures II: Torture Trouble

Atari 5200: Mario Bros.

Nintendo Nes: Super Mario Bros 3

Gameboy: Super Mario Land 2

TurboGrafx-16: Vigilante

Sega Megadrive: Streets of Rage 2

Super Nintendo: Super Mario Karts

Neo Geo: Shock Troopers

Atari Jaguar: Doom

Playstation: WCW vs the World

Nintendo 64: Goldeneye 007

Sega Dreamcast: Soldier of Fortune

GBA: Double Dargon Advance

Playstation 2: Fire Pro Wrestling Returns

Nintendo Gamecube: Pikmin 

Xbox: Driver 3

Nintendo DS: Super Mario 64 DS

Xbox 360:  Nothing.

Nintendo Wii: Super Mario Galaxy

Nintendo 3DS: Valet Parking 1989

NES: Mario 3
SNES: Turtles in Time
N64: Mario 64
Cube: Smash Bros. Melee
Wii: Smash Bros. Brawl
Game Boy: Pokemon Red
Game Boy Advance: Mario and Luigi: Superstar Saga
DS: Elite Beat Agents
3DS: Resident Evil Revelations

Playstation: Small Soldiers
Playstation 2: Kingdom Hearts 2
Playstation 3: Heavy Rain
PSP: Kingdom Hearts: Birth By Sleep

Xbox: Three-way tie between Halo: Combat Evolved, Breakdown, and Knights of the Old Republic
Xbox 360: way too many to pick just one... Arkham City, Mass Effect, Gears 3, Reach, and Left 4 Dead 2 would be my top picks.

Mine are:

Atari - never actually owned the game, but played it after and it's H.E.R.O. Very modern game for its time.
Master System - Alex Kidd in Miracle World
NES (called Phamtom System here) - Super Mario Bros 3
Genesis - Toe Jam & Earl / Sega CD: Sonic CD
SNES - Super Mario World
Game Gear - Streets of Rage 2
Gameboy - Only had one game so, by default... Pokémon Yellow
Dreamcast - Mars Matrix and Giga Wing
PS2 - Metal Gear Solid 3
Gamecube - The Legend of Zelda - The Wind Waker
DS - Hard to choose but a tie between New Super Mario Bros and Animal Crossing

Wii - Had it just for a short period and didn't played it much, but New Super Mario Bros Wii
PSP - Megaman (s) and Ultimate Ghouls and Ghosts
3DS - Mario 3D Land.. no... Kid Icarus... no, 3D Land... no, Kid Icarus....TIE!!!!

And N64: The Legend of Zelda - Ocarina of time. Best overall too.

So cool to see a fellow Sega Saturn owner, there aint many of us.

Master System: Sonic
Gamegear: Sonic
Gameboy: Pokemon Blue/Red
MegaDrive: Sonic 2
Playstation: Syphon Filter
Gamecube: LoZ: Wind Waker
Xbox: Black
GBA: Pokemon Ruby/Sapphire
DS: Pokemon Black/White
Wii: LoZ: Skyward Sword
Xbox 360: Mass Effect
3DS: Kid Icarus: Uprising

It was my first console, there were so many games I had for it as my dad was a games dealer, but he sold most of them when he gave it up. We even had Panzer Dragoon Saga at one point.

I was too young to remember most of the games, but NiGHTs into Dreams was still vivid in my mind, even though I hadn't seen anything to do with it since the age of 3. I rumaged through my dads barn and found the Sega Saturn along with loads of other games a few years ago, I've had it set up in the front room ever since.

Yeah I've only played a few PS1 games in total and Tomorrow Never Dies was by far my favorite. I had so much fun with that game (even though I sucked really bad at it and died so many times)