Many of the converters eg. Super DVD Creator, WinAVI Video Converter, etc, now available can convert all the avi files that I have downloaded via Limewire. The probem is usually that you may not have the audio and/or video codecs installed for the particular avi files. A sure sign that you don't have the necessary codecs is when you could not preview the file in your Windows Media Player or Limewire player.

What you can do is go the this site and download and install the latest codecs until you can preview the avi file either in Windows Media Player or the converter that you are using.
http://www.free-codecs.com/