Right now, my favorite WordPress plug-in for playing MP3s is MP3-jPlayer by Simon Ward. I use it on the sidebar to the right on this very site to play some of my original music.
The only issue I have is an annoying 40px bottom padding that is put on the playlist player. The CSS has gotta be hard-coded somewhere, but I found a simple fix that I’d like to share:
On your WordPress dashboard, go to Appearance > Edit CSS and add the following CSS code:
padding-bottom: 0 !important;
This will override the inline style code for the player object. I’ve set it to zero, but you can change to whatever works for you.
On a side note, this wonderful plug-in seems to have disappeared! I hope it returns with new revisions. Simon’s own site says you can download from WordPress but the link is broken and the plug-in seems to be missing even if you search for it :-(