Songbird Frees the Music Player
You can think of Songbird as a sort of mashup of web browser and desktop music player. It can play music files (Ogg Vorbis, MP3, FairPlay, AAC and a variety of other formats) from your local system or from a web page. To Songbird, any web page is a potential playlist; if there are music links there, you'll see them displayed in a separate window with easy buttons for download. Songbird also understands some other web formatting, so if you browse to (for example) The Hype Machine, you'll get buttons to buy songs in the playlist.
Being built on the Mozilla core, Songbird understands skinning (Songbird skins are called "feathers") and add-ons. For example, you can install an extension that reads your existing iTunes library into Songbird, or one that displays the Wikipedia page for the currently-playing track.
The current Songbird release is version 0.4, which you can download from their Developer Center. If you'd like to be a bit more on the cutting edge, you can opt for the just-released 0.5rc1, which adds MTP device support on Windows. Although the application is still in beta with some bugs, it's quite usable and under rapid development.
Have you used Songbird? Would you say it competes with the non-OSS music players?