Download VLC. It will play pretty much every media file you come across, except Real and Windows Media. If you really want to use Quicktime, you'll have to poke around and find the right codec to install... which I wouldn't recommend.
I suspect that you downloaded the 3ivx codec. To play the audio track with this codec, .avi files with .mp3 audio tracks require conversion with DivX Doctor II. DDII is available with from the 3ivx.com website. If you install the DivX 5.2.1 or DivX Fusion (DivX 6 beta), you can play the .avi files without conversion. Unlike the VLC player, the DivX codec will allow you to use .avi files in all of your QuickTime-compatible applications.