It's called SongSmith. It's a computer program where you sing into a microphone, it records the song, then comes up with an accompanying instrumental track.
The music it composes works with the vocals on a purely logical level: it follows the beat and tempo competently, and it actually sounds like music (just not very good music).
People have taken popular songs, isolated the vocal tracks, and then run them through SongSmith. The results have been...well...you should probably just listen for yourself.
I downloaded the trial version of SongSmith, and I've been looking into ways to isolate vocals from MP3s.
Apparently it's fairly easy to remove the vocals, but far more difficult to remove everything else and leave the vocals behind, especially with free software.
That's too bad. I really wanted to make some of these.