With PlayStation, I honestly dont think the games i would mention actually define my experience with the platform. But thats cause Sony has a way of bringing in new franchises often. so I'll just go with

GT, Jak, Uncharted, killzone, GoW and I'll throw in Final fantasy and kingdom hearts. Therr are tons more, but thede all have a certain significance to me at certain times in my life.

For Nintendo, I think of them and all i see is super Mario bros on the NES, metal gear, Zelda and Fzero.

As for Xbox, its never been my thing. But if there is anything i can think of it would be KotOR and splinter cell.

Nintendo: Mario, Zelda, Pokemon, Pikmin, Star Fox

Sony: Crash, God of War, Ape Escape, Gran Turismo, Sly Cooper

Microsoft: Halo, Forza, Fable, Banjo Kazooie, Conker

Edit: This was a list of the first five games i could think of. If it was a list of the reason why I like the company it would be like this:

Sony: Crash, God of War, Sly Cooper, Ape Escape

Microsoft: Banjo Kazooie

Nintendo: Smash (with almost everyone inside, so no one is missed :p)

The ones that I could think of quickly when thinking about each of the big 3 are:

Playstation:

Uncharted
LittleBigPlanet
God of War
Gran Turismo
Heavy Rain


Nintendo:

Mario
Pokemon
Zelda
Super Smash Bros.
Donkey Kong

Microsoft:

Halo
Gears of War
Forza
Alan Wake
Fable

Playstation: God of war, Uncharted, Ratchet and Clank, Gran Turismo, inFamous (stopping myself here)

Nintendo: Donkey Kong, Mario (smash, 2d, kart, 3d)

Microsft: Gears, Halo, Forza, Crackdown, Fable

I just think of Nintendo as I'm a Nintendo gamer,

I think of Xenoblade, Mario, Zelda, Fatal Frame, and Bayonetta.

Playstation: Uncharted, Metal Gear Solid, Final Fantasy, God of War, Suikoden.

Nintendo: Mario, Mario Kart, Smash Bros, Zelda, Pokemon

Xbox: Halo, Gears of Wars... Forza I guess? Game 4 and game 5.

Nintendo: Super Mario, Smash, Pokemon, Zelda, Fire Emblem

Sony: Uncharted, LittleBigPlanet, The Last of Us, God of War, Gran Turismo

Microsoft: Halo, Gears, Forza, Fable, Minecraft?

Nintendo: Mario, Zelda, Kirby, Fire Emblem, and Metroid

Sony: Crash, Uncharted, GT, The Last of Us, .....

Microsoft: Halo, Banjo, Gears of War, Perfect Dark, Crisis

Nintendo: Zelda, Mario, Fire Emblem, Metroid, Pokemon

Sony: Uncharted, God of War, Crash, The Last of Us, Final Fantasy

Microsoft: Halo, Forza, Gears of War, Banjo, Fable

Nintendo: Mario, Zelda, Pokemon, Donkey Kong, Metroid

Sony: Ratchet and Clank, Uncharted, God of War, Infamous, Gravity Rush

Microsoft: Halo, Gears of War, Forza, Fable