Song.ly is a new service built around twitter for sharing MP3s with your twitter followers. Song.ly takes URLs of mp3 songs hosted on twitter and converts them into short urls and also allows users to play them in a flash player.
The service is simple to use, just enter URL of the song to share in song.ly and it gives you the shortened URL which you can tweet. Your twitter followers can play it in the little flash player. It displays original URL of the mp3 file, so they can download the song immediately.
There is a Firefox add-on available if you want to use it regularly. The add-on is experimental so you need to login to Mozilla site to download it. With the Firefox add-on you can right click any mp3 you find on the web and Share it with song.ly.
This is the simple and useful service to share mp3 files twitter way. The missing feature is the ability to upload mp3s, may be it is intentional because it will land them in legal troubles.