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Quicktime will. You click on File>Export and select Movie to iPhone or iPod or whatever. But you don't need to, you can open AVI files on iTunes anyway. Just right click, select Open With and then choose iTunes.
 
Open them with quicktime and save as a reference movie. This will create a small pointer file which you can add to your iTunes library.
 
I had this problem too.

I tried through Quicktime, but my problem was that there was no audio in the movie when I played it through Quicktime. I assume I had a codec problem even though I thought I installed everything.

Anyways, I ended up just downloading AnyVideoConverter (PC only - shudder) and ran it through VMWare. Really a pain though.
 
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