ipod classic back scratched.

Here are some ways to remove scratches...
Ice Creme
iCleaner

Also, here are some reviews...
Applesauce Products Scratch Removal Kit for iPod
Battle of the iPod polishes: iCleaner vs. Ice Creme
PodShop iDrops
Radtech Ice Creme Version 2 Scratch Remover
RadTech OmniCleanz
Reckitt Benckiser Brasso Multipurpose Metal Polish

Some of those links might be outdated, but see what you like!

btabz

First of all, I curse Apple for not making the whole thing brushed silver like the front of my silver one is, instead of putting that awful finger-print magnet chrome on it.

So what I did was put a piece of screen saver plastic over the whole back. You hardly notice it's there, though it does cut down on the shiny mirror like finish. BUT it gets rid of the gathering of fingerprints, so to me it's totally worth it. AND it will prevent further scratches.

I put mine in a leather case and the first time I ever took it out, to load it in my new dock, it immediately somehow, magically almost, got a bunch of small scratches on the back - even though I was super careful not to get any.

So my advice is, if you do get the scratches out, use a clear plastic screen saver that they recommend for screens of digital cameras, on it. It's a bit tricky to learn to apply them without fingerprints or bubbles, but it can be done if you practice.