Hoo boy, might have to think about a few of these...
N64: Super Mario 64 and Paper Mario (I know you said only one, but these are two of my all-time favorite games... Couldn't bear to leave either of them out!)
Gameboy Color: Pokemon Gold
Gameboy Advance SP: Pokemon Ruby
Gamecube: Paper Mario: The Thousand Year Door (though Tales of Symphonia runs it a close second)
Xbox: Fable (Say what you will about its sequels, but I had a ton of fun with this one)
Playstation 2: Kingdom Hearts! (Love the second game, too)
DS: The World Ends with You and Chrono Trigger DS (Again, two of my all-time favorites, and I'd never played Chrono Trigger before the port)
Wii: Xenoblade Chronicles (Haven't quite finished it yet, but I'm really close... Won't be able to play it for another 8 months though -_-;)
Xbox 360: Enslaved: Odyssey to the West (More people need to play this!!) and Lost Odyssey are tied for me.
Edit: Forgot about the PSP, 3DS, and PC.
PSP: Kingdom Hearts: Birth by Sleep was my favorite there.
3DS: So far, Legend of Zelda: Ocarina of Time
PC: Guild Wars!!
Hmm
