I bought the wife a 20gig ipod photo to take to work, we got the music to the ipod, but i would like to back the music up to my computer downstairs, and also listen to it on my computer downtairs.

That behavior is a built in "security feature" keeping people from loading up their iPods as portable harddrives and copying them to multiple computers. I tend to keep all of my music in one folder that I back up to data DVD, that way I have options in the event of loss. In order to listen to the iPod on the downstairs computer, you can hook it up via the USB cable, install iTunes and listen through that computer's speakers. I listen to my iPod via my computer and headphones every day at work.

Hope this helps!

(I might add that there *may* be some hacking type software to remove the restriction of copying... I've not yet found any that was worth anything decent, though)