I've posted my favourite games rather than what I believe were the definitive ones, simply because I could mention games that meet the latter without having played them - e.g. I've never played Samba Di Amigo or Radiant Silvergun but I'm sure they would make any most definitive lists.
In order of the consoles I've owned:
Atari 2600:
Dig Dug
Combat
Spiderman
Pac-Man
Master System (Mk2):
Alex The Kidd in Miracle World
Sonic The Hedgehog
Sonic The Hedgehog 2
Castle Of Illusion (preferred the MS version to MD one)
Operation Wolf
Mega Drive:
Streets Of Rage 2
Strider
Sonic The Hedgehog 2
Gunstar Heroes
Dynamite Heddy
Splatterhouse 2
Micro Machines 2
ThunderForce IV
Quackshot
Road Rash
Super Nintendo
There are far, far too many amazing games for the SNES that I'm just gonna stick to ones beginning with "S"! I could have a list of 50 games and still not be able to list all my faves! Needless to say,this was my favourite console of all time.
Super Metroid (best game ever!)
Super Mario World
Super Mario All-Stars
Starwing
Stunt Race FX
Super Mario Kart
Super Street Fighter 2
Super Castlevania IV
Super Bomberman
Super Punch Out!
PlayStation
Wip3out
Resident Evil
International Track and Field
Final Fantasy VII
Tomb Raider
Destruction Derby
Gran Turismo
Metal Gear Solid
Rage Racer
Tekken 2
Saturn
Nights
Burning Rangers
Guardian Heroes
Sega Rally
Fighters Megamix
Street Fighter Alpha 3
Virtua Fighter 2
Virtua Cop 2
Virtual On
Xmen Vs Street Fighter
Nintendo64
Super Mario 64
GoldenEye
Mario Kart 64
Lylat Wars
Zelda: Ocarina Of Time
Donkey Kong 64
Banjo-Kazooie
Blast Corps
Jet Force Gemini
Super Smash Bros.
DreamCast
Shenmue
Crazy Taxi
Soul Calibur
Dead Or Alive 2
House Of The Dead 2
Metropolis Street Racer
Power Stone
Resident Evil Code Veronica
Street Fighter III: Third Strike
Virtua Tennis
Xbox
Halo
Halo 2
Beyond Good & Evil
Burnout 3 Takedown
Street Fighter Anthology
Pro Evolution Soccer 4
Splinter Cell
Knights Of The Old Republic
Ninja Gaiden
Prince Of Persia: Sands Of Time
GameCube
Zelda: Wind Waker
Donkey Konga
Ikaruga
Metroid Prime
Paper Mario: Thousand Year Door
Rogue Squadron II: Rogue Leader
Wario Ware Inc
Animal Crossing
Viewtiful Joe
Tales Of Symphonia
I have a PS2 as well but I've played so few games on it that I couldn't really make a top 10 (probably struggle with a top 5 in fact!)
EDIT: Forgot about PC and handhelds, but I think this list is long enough as it is.
