I guess I bought a Wii for Zelda, and a DS for Pokemon, but that's it. But that's mostly because I hardly ever use those consoles for anything else. I don't even use my DS at all any more since I've more or less gone off Pokemon. Also, those consoles are rather cheap, so it's not a huge investment.
I find it harder to justify buying any of the other consoles on one game alone. Usually it's a group of games. The reason I bought a 360 was pretty much just because it was so much cheaper than a PS3 at the time, and had a better library, but none of them were worth carrying the console on it's own. It has some good exclusives (Forza, Gears of War, Halo) but they are few and far between. Also there's usually a comparative game available for the PS3. That works both ways of course. I always try to justify buying a PS3, but I can never manage to actually make it enough to buy one myself. It does have great games like God of War, Ratchet and Clank, Gran Turismo (although from my experience I'm rather unimpressed with GT5), Resistance, Uncharted etc., but I still can't think of any game that I really have to own and cannot get a similar game on 360. I suppose there's God of War, but I can live without that. Recently the stuff that's drawn me towards a PS3 are the HD re-releases of PS2 games, but I already have a PS2 so it's a bit pointless.