.avi files should be playable in the Windows Media Player, IrfanView, Winamp and many others. However, browsers need to know this; if they have never been told how to handle .avi files, they just give up.Mozilla isn't as smart as Internet Explorer when it comes to plug-ins. If you know the file extension and MIME type, you can specify which plugin Mozilla should use (go to Edit > Preferences... Navigator > Helper applications).
Web designers can help out by specifying the pluginspage attribute for the file: the value is a URL from where the user can download the appropriate plug-in. It's also a good idea to include a normal link on the page ("To see this movie, download the XYZ plug-in here").
Another approach is to link not to a page with the video file embedded in a web page, but to the .avi file directly. Internet Explorer users are usually presented with a dialogue asking if they want to download and save the file, or open it in the default application; Mozilla users can right-click on the link, choose "Save Link Target As..." and save it to the hard disk. They can then use whichever media player they prefer to open the file.