Removing CD Scratches... The Cheap-Ass Way
One of the cheapest, yet still effective, methods for removing scratches from CDs and DVDs is to use toothpaste. I haven't been able to find the principle behind it, but it works. It's basically the turtle wax method that Lobsang Rampa described above, but with toothpaste instead of turtle wax. You apply some toothpaste to a soft, lint-free cloth, gently rub it onto the CD from the center to the border and back in a radial manner (NOT sideways or circularly), let it sit for just a couple minutes, and then rub it off with a fresh piece of lint-free cloth in the same radial manner.
There are only a few differences from the turtle wax method. The first is in your choice of toothpaste. The jury seems to be out on whether or not to use toothpaste that has baking soda in it. Patrick Norton from The Screen Savers recommended baking soda toothpaste. It worked for him and it worked for me, but a lot of sites tell you not to use it for vague reasons. The one thing that just about everyone can agree on is that you should not used colored toothpaste, toothpaste with gel in it, toothpaste with exotic additives, or generally anything besides plain white toothpaste and plain white baking soda toothpaste. Anything else is pointless crap that doesn't do anything for your CD, but some of it can make the process of removing the toothpaste much harder.
The other possible difference is that the data side of discs with a lot of scratches on them, like the ones that you get from Blockbuster or other rental stores, are probably going to look like absolute crap after you use this method. I haven't heard much about this from the people that have recommended turtle wax or toothpaste, but the DVD from Blockbuster that I repaired came out with a permanent dull white coloring that was highlighted in the scratches. Regardless of this, the toothpaste method repaired the DVD and turned a scratched hunk of plastic back into a PS2 game.
Oh, and if you're worried about using the cheap-ass method, just about everywhere that I've looked has told me that turtle wax, toothpaste, and scratch remover all work roughly the same, so if toothpaste doesn't work, you were probably going to end up with a useless hunk of plastic anyway. YMMV, though, so be as cautious as you feel comfortable with.