I bought my PS3 just to play Final Fantasy Tactics. Yes, you heard that right.

I had a mod chip added to my PS2, but as a side affect it rendered it unable to read CD's. I bought on of the old hardware emulation PS3 models just so I could play a PS1 game.

Other than that I would never buy a console just for one game, but the threshold of games I need to own one is rather low. I only buy 5-10 games for most consoles I have.