(There is an updated post at Click to hear the MP3 playlist (Apr 2006))

When you want to have an embedded player in a web page, there are several options: working with an embedded RealPlayer or WindowsMedia player – which do not all work on a Mac/Linux platform or with Firefox. Another option is using a Flash player. Flash/ShockWave is supported on all platforms and in all browsers. I went on a search for free embedded Flash players:

SoundBlox
License: This is an Apache-style open source project by Laszlo Systems, based on the Laszlo open-source RAD framework. It is free for non-commercial use.
Method: you reference a Javascript file in your HTML headers, and then call a Javascript function with the URL of the playlist. (This is a problem for some sites. Blogger e.g. does not allow <script> tags in its posts, only in the template.)
Format: it uses a proprietary XML format. <geek>Files in XSPF format can be converted to the SoundBlox format through XSLT</geek>
MusicPlayer
License: This is an open-source (SourceForge) project by Fabricio Zuardi. It is free for non-commercial use.
Method: you reference a Flash file and give it the URL of the playlist. The Flash file is embedded with the usual <object> and <embed> tags.
Format: it uses the standard XSPF (XML Sound Playlist Format). Webjay can convert any HTML file/feed to XSPF!
Check my Webjay wizard to generate the right HTML code for your page!
Halfbaked
License: not explicitly stated. I presume it’s free to use.
Method: you reference a Flash file and give it the URL of the MP3 file. The Flash file is embedded with the usual <object> and <embed> tags.
Format: No playlist here, just one MP3 file.
GurusNetwork
License: not explicitly stated. I presume it’s free to use.
Method: you reference a Flash file, which contains the playlist of the MP3 files to play. You can’t specify a self-made playlist
Format: No idea.
Sonify
License: not explicitly stated. I presume it’s free to use.
Method: you reference a Flash file, which contains the playlist of the MP3 files to play. You can’t specify a self-made playlist
Format: No idea.
RadioBlogClub
License: free to use.
Method: you host the player with all graphics and a config.xml file, that points to a playlist.
Format: A PHP script creates an XML playlist for all MP3 present in a local(!) folder.

For more information on playlist formats (XSPF, SMIL, ASX, …), check out Lucas Gonze’s excellent survey.

There are also some commercial options: hooverwebdesign.com ($50), wimpyplayer.com ($25), soundnails.com ($15)