Games that personify/define a console to you

[Alex_The_Hedgehog]

NES - Super Mario Bros. 3

SNES - Super Mario World

N64 - Super Smash Bros.

PS1 - Crash Bandicoot 3

PS2 - God of War II

GC - Luigi's Mansion

3DS - Mario Kart 7

Wii - Super Smash Bros. Brawl

WiiU - Super Mario 3D World (Or Mario Kart 8, not sure)

Most of those were the first games I played on the system, so that's why I relate.