you are thinking of other players that don't play mp3 files, generally they only play a single file type that you can only get from a single program, those types of players that lock you in are a complete waste of time and money (they normally insist you pay for every song you want, and because you have 2 choices of either pay them or not listen to anything, they also charge stupid prices) - the ipod is the only common one i know of with that problem of insisting on using their software, and then they still allow you to import your own mp3 files as far as i'm aware
any mp3 player will play any mp3 file, mp3 files downloaded from winmx are not in any way different to mp3 files downloaded from some other program, or ripped from a CD yourself