This is the player i use on my site, works in IE aswell as in FF.
It's a flash one so it does have it's limitations on what soundfiles you can use.
From the README.TXT:
HINTS
the mp3 player only accepts mp3 files. support for other audio formats is impossible. also, flash doesn't support vbr (variable bit rate) mp3 files. if you play vbr mp3 files, the playback will sound like a chipmunks version of your songs. the best way to encode mp3 files is to use a fixed bitrate of 64/96/128 kbps with a sample frequency of 22.05 kHz and joint stereo.
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