NES: Super mario bros
master system: wonder boy in monster land
turbografx-16: Ys book I & II
Genesis: Streets of Rage
gameboy: Pokemon red/blue
SNES: Super puyo puyo
Sega Saturn: Radiant Silvergun
PSX: Tekken 2
N64: Super Mario 64
Dreamcast: Phantasy star online
PS2: Virtua Fighter 4 evolution
Gamecube: Phantasy star online ep I & II
Gameboy Advance : Golden Sun
Nintendo DS: Animal Crossing Wild World
Xbox 360: Grand Theft Auto 4
Wii: Animal Crossing city folk

Oh damn.

GameBoy: Pokémon Blue
GameBoy Color: Link's Awakening
GameBoy Advance: The Minish Cap

Sega Genesis: The 6-Pak

THIS IS IMPOSSIBRU

N64: Harvest Moon 64
GCN: Pikmin
Wii: Smash Bros. Brawl

*brain explodes*

Hang on I forgot one

3DS: Kid Icarus Uprising

*dies*

NES: Teenage Mutant Ninja Turtles 3
GENESIS: Sonic the Hedgehog 2
SNES: Pocky and Rocky 2
PSX: Final Fantasy IX
SATURN: Panzer Dragoon
N64: Conker's Bad Fur Day
DREAMCAST: Jet Grind Radio
PS2: Yakuza 2
XBOX: Halo CE
GC: MGS Twin Snakes
XBOX360: Halo Reach
PS3: Yakuza 3 (and 4)
Wii: No More Heroes 2
PC: Duke Nukem 3D
GAMEBOY: Pokemon Silver
GBC: Zelda Oracle of Ages
GBC: MegaMan Battle Network 2 (and 3 and 6)
PSP: Final Fantasy Crisis Core
3DS: Zelda Ocarina of Time 3D

3DO - Need For Speed (also the only game we had)

PS1 - Either Gran Turismo 2 or Crash Bandicoot 2/3

PS2 - Star Wars Battlefront or Gran Turismo 3 perhaps (SOCOM 2 deserves mention as well)

PS3 - Uncharted Drake's Fortune (I like it better than U2) and also Resistance Fall of Man

360 - Call of Duty 4 and Fallout 3

PSP - NFS Underground (I don't have many for it)

All Nintendo Handhelds regardless of generation - Pokemon Red

Gamegear - I don't really remember what we had for it, I think some Sonic games and shit

Wii - (my parent's console not mine) New Super Mario Bros Wii, but I also like Mario Party 9...it makes an amazing drinking game (gain stars and you give out drinks, lose stars and you drink...and at the end give out more drinks depending how you placed)

This is tough.

Genesis, Sonic2
N64 got this one a little late but Majora's Mask
PS1 Crash any of them
PS2 MGS3
PS3 Uncharted 2
GB Mario Land2
GBC i think the only ACTUAL GBC game i had played was Link's Awakening DX so that one
GBA BOF2 tied with FF6Advance
DS the world ends with you
3ds so far Mario 3d land
PSP KH BBS
PSVita Gravity Rush so far
GC Melee
Wii Goldeneye played this game the most by a country mile

i love this kind of threads

home consoles

Genesis: Sonic
SNES: Super Mario World
PSX: Resident evil: Directors cut
N64: so difficult to just get one; Mario64, Zelda MM, Zelda Oot, Pefect dark, Goldeneye, Turok 2, Banjo, CBFD
PS2: GT3 A-spec
GC: bufff.....i would say.......Metroid prime
Wii: Zelda SS

handhelds

GB: DKLand 2
GBColor: Zelda oracle of...
GBA: Mario tennis Power tour
NDS: SMario 64 DS (with all the great new games that came for the DS...this game is just that good)
PSP: DBZ tenkaichi tag team
3DS: RE Revelations

NES: Ghosts 'n Goblins
Mega Drive: Flashback
PS1: Tomb Raider 1
N64: CBFD, Rayman 2
PS2: GTA San Andreas
PS3: Journey

new - THE LEGEND OF ZELDA
snes - SUPER METROID
n64 - SUPER MARIO 64
sdc - HYDRO THUNDER
ps2 - RYGAR THE LEGENDARY ADVENTURE
xbox - HALO COMBAT EVOLVED
ngc - SUPER MARIO SUNSHINE
x360 - ELDER SCROLLS OBLIVION
wii - SCAREFACE WORLD IS YOURS
ps3 -ASSASSINS CREED II
nds - BRAIN AGE
psp - VICE CITY STORIES
gb - METROID II
gba - SUPER MARIO BROS. 3
3ds - PILOT WINGS RESORT
psv - MORTAL KOMBAT

I cant really decide I just name some games i really really like instead!

Commodore64    
  Mario Bros (so long ago thats the only game I remember the name of LOL but as far as I remember I played it a lot and maybe FlaschBier)

NES    
  Super Mario Bros3, TMNT 2 Arcade

SNES  
  Terranigma/ Secret of Mana/ A link to the past, TMNT Turtles in Time (I do have a mint copy of chrono trigger but never played it)

PS1 (was my sisters console she had all the RPGs so I could buy other stuff)
  KKND Crossfire (coop), C&C Red Alert + addon (LAN mode), GTA 1  (I bought Alundra 1 year ago haven't played it yet)

N64    
  Ocarina of Time/Majoras Mask/PerfectDark/Goldeneye/Smash Bros

DC (I have this console for a month or so now thats my only game so far LOL)
   Dead or Alive 2

PS2
   Dead or Alive 2. Dragon Quest 8. Rogue Galaxy

GC
   Wind Waker. Tales of Symphonia, Skies of Arcadia, Metroid Prime

Wii
   Xenoblade, Skyward Sword, SSB Brawl,

360
  Dead or Alive 4,  Tales of Vesperia, Halo Reach

PS3
  Tales of Graces F, Yakuza 4.

Didn't include handhelds here would take another hour for me to decide.  (Btw I have a ton of PS3 and 360 and Wii games I didnt even start so I have no real idea which of the games will become my favorites)

N64 Banjo Kazooie
PS1 Final Fantasy IX
Gameboy color: Pokemon Silver
Gamecube: The Legend of Zelda Windwaker
PS2: Final Fantasy X
Gameboy Advance: Fire Emblem
DS: Pokemon Pearl
PSP: Final Fantasy Crisis Core
PS3: Fallout 3
Wii: Super Mario Galaxy
3DS: Super Mario 3D Land