SNES for me has to be Starfox, as it was the game that came with the system for me, and its spirit of bold ambition and taking the first steps into the 3D realm is a big part of the Super Nintendo's personality for me.
N64 would be Banjo Kazooie, as Rare's output on the system was a huge part of the console's appeal for me, and of those BK was the most quintessential.
Wii, gotta be Super Mario Galaxy, that game's freewheeling sense of innovation and adventure summed up what I loved most about that era of Nintendo.
Wii U, Splatoon. Its the main thing to come out of that generation that felt new and of the time rather than a continuation of past trends.
PS1 will always make me think of Crash Bandicoot; I didn't have a PS1 growing up so I mostly played it when visiting friends and family, and this was the first game on it that hooked me.
PS3 has to be Uncharted 2, it was such a huge event when it came out and finally made the PS3 feel worthwhile.
Xbox 360, probably Gears of War, as the game that first showed what a huge leap it was over the previous generation, and which set the tone for much of the generation that would follow.