Most of the commercial products are either optical-equivalent patching compounds or polishers. Obviously, you'd have to buy something to get optical equivalence. So you're left with polishers. The polishers I've used don't even require that the disc be unscratched afterwards. You just need to get rid of severe radial scratches. Most of them still appear as if you've gone after them with steel wool afterwards. (And, yes, they do work, or at least make the CD work better.) So you could find a polising agent around the house. Maybe some metal cleaner like Brasso? (I suppose any petroleum products might dissolve the plastic, though, which is probably a bad thing.) Toothpaste makes sense. Maybe a baking soda paste? I've also heard peanut butter.

You might want to scratch a crap CD (do you get AOL ones in the mail over there?) and test any method out first before completely ruining a hard-to-replace CD.