This will clean all the dirt and fingerprints off and remove a lot of the yellowing that comes from many years of absorbing the atmosphere.
(The author used Sun Light Gel by Lever Brothers, but other detergents may work.)
There have been some discussions on some of the other LEM lists, like the Compact Mac list, that mention cleaning some very smoke yellowed compact case with detergent and bleach and leaving them out in the sun. (Careful, this could damage the plastic.)
Source: Dan Pennington, Brooklyn Park, MN / LisaList 2003.09.23[LisaFAQ] > [Hardware] (Comment on this answer)