I have some potentially great songs which are spoilt by singers who sing out of tune. Is there any easy to use (and hopefully cheap) software that 'corrects' the song so that they're not off-tune anymore? I don't mind too much if the backing is somewhat affected too, if the state-of-the-art isn't quite there yet.

I've heard of auto-tune of course, but as far as I know, that's before the song is put together (i.e. the singer's voice as an individual track, before it's mixed with the backing).