I think that's what iTunes is "supposed" to do. My understanding is that there is one authorized computer and you can change that to a different computer, but you can't sync songs from both simultaneously. I could be wrong, since I haven't ever owned an iPod or used iTunes though.

Anyway, here's how I did it on Linux:
I got <a href="http://www.ephpod.com/">EphPod</a> (which is actually a Windows application that works surprisingly well under WINE ), and used that to grab any songs I wanted from the iPod in question. Then I had some mp3 files, some m4a files and a whole bunch of m4ps. The m4ps are the protected files, so I downloaded <a href="http://hymn-project.org/">Hymn</a> (also a Windows application) and ran each of the m4ps through that, which decrypted them very nicely. For good measure, you can convert them to mp3 in the same step by clicking the "Convert to mp3 as well" checkbox.

In summation, it was pretty much a two-step process to grab songs from an iPod and remove the DRM and convert to mp3.