Unfortunately, the shiny chrome backside of the iPod Classic and iPod Touch scratch with even the tiniest bump against a hard surface, and while lots of less aesthetic-minded people will tell you to just "suck it up, it's not a big deal", the rest of us know that the wound to our little electronic friend cuts us deep to our very core )= A simple Google will show that you are not alone--thousands of people are constantly searching for a way to repair the cosmetic damage to the backs of their iPods.
Some people will feel the need to snarkily comment "just put a case on it!" I have--and plan on--putting my newly buffed iPod in a case, but there are a variety of reasons you may have gotten a scratched iPod, from buying a secondhand player to an improperly fitting case, as was the situation with mine. Or perhaps you just like the naked look better.
Through a lot of trawling through the internet, I've found a lot of supposed solutions, ranging from polishes (popular ones are Brasso, Applesauce, and Ice Cream) to more hacker-y ones like the "banana method" or toothpaste. Whether or not these work, I can't say--I haven't tried any of them.
This method is more about smoothing out and camouflaging scratches than about filling them in, as most of the above alternatives are for. Because let's face it--scratches on the backs of iPods are just one of those things in life, like papercuts and celebrities doing panty shots while getting out of the limo. And no matter how many times you apply polish to the back of your iPod, the scratches will always come back.
The best thing about this method, in my opinion, is that it doesn't require any fancy equipment or expensive supplies. I see a lot of beautiful and amazing projects on this site and click on them eagerly, only to see that they require a laser cutter or flame thrower or something to execute. I'm an art student, not a trust fund baby. I can't afford your fancy equipment! So while I completely appreciate the sharing of such amazing projects, they really do nothing but give me frowny faces.
This Instructable has the same basic concept as the Brushed Steel iPod Back Instructable, but with a key difference--you'll be able to keep the Apple logo and serial numbers on the back, as well as any laser etching you may have gotten on it, and you'll still be able to use your iPod as some kind of weird, distorting funhouse mirror. This method also has less risk of damaging your iPod, as it uses a milder abrasive than the Scotch Brite pad/sanding block combo.
Please note that this is not a technique for the original mirror-smooth finish--It gives a softer, shinier "brushed" finish for those who can't stand those appearance-marring scratches but don't want to change the look of their iPod completely.