Never had a console just for one game. To be honest it doesn't seem like a good use of money (depending on how cheap it is) to use a console for one game.
Even if I did get it cheap I'd try to see if there are any good games I can pick up to get more bang for my buck.
In fact if I didn't want to get LittleBigPlanet for my PSP, I probably would've never picked up Soul Calibur. Or if I didn't get LBP for the PS3, I'd be missing out on great games like Uncharted and InFamous.
Not necessarily for single games, but the only reason I bought a Nintendo 3DS, and the only reason I intend to buy a PlayStation Vita and Wii U, are to keep up to date with my reviews. I literally bought my Nintendo 3DS a week before my copy of Kid Icarus: Uprising came in just so I could review that game.
somewhat relevant, the only reason I went out of my way to reclaim a PlayStation 2 was to play Okami. Now I have a few more games for it, so time and effort well spent.
I bought a PS1 to play Rayman. Right now the only PS1 games I have are Rayman and Chrono Cross, but there actually are a lot of other games I would like to get (although the used game store near my house doesn't have a good selection of PS1 games). I am looking forward to getting Castlevania: Symphony of the Night, a few Final Fantasy games, Frogger, and some others.
I got a PS2 to play Kingdom Hearts. Didn't like the game, but I made my PS2 more worth it because I later bought Final Fantasy X, Final Fantasy XII, and Rayman 3.
My PS1 is also currently collecting dust now that I have a PS2 the is backwards compatible.
I had a Genesis and the only games I had on it were Sonic 2 and some Aladdin game, which was actually fairly decent from what I recall. I remember buying a Gamecube back in '02 just for Sonic 2 Battle as well.