As far as I know, music purchased at the iTunes Music Store is protected with DRM called "FairPlay" that only Apple's iPods can use.
You could always burn your purchased iTunes store music to a music CD and rerip it back to your computer, but I guess there's some quality loss with that, plus you have to reenter the songs name, artist, etc.
There is also another newly released program that's supposed to remove Apple's DRM, but I haven't played with it myself.