All iPod's can pretty much only read movie files in .MPG-4 format. I think they can run .MOV and .3GP2, but .MPG4 is the most reliable.
There are numerous converters on the web, but they all cost a pretty penny. Even the ones that claim to be "free" will either only convert a portion of the video or will have an annoying watermark in the middle of the video.
Here's what you do.
1.
Download RealPlayer SPRealPlayer has a built-in convertor which works wonderfully and can convert pretty much any file to anything. It also has an option which will allow you to download any video you find on the web, even YouTube (just be careful of copyright laws in your region).
2. In the convertor, drag and drop the AVI files you want and choose the option to "Convert for iPod".
3. Add the files to iTunes in the usual method.
4. Enjoy.