I also have a Logitech G15. It's fairly new so it's not dirty yet, but I occasionally wipe the outside with tissue and alcohol. I play Warcraft 3 and sometimes my fingers sweat so much when I play. Haven't cleaned the inside though.
I also clean my mouse often, coz of the sweat. I even opened my Razer Copperhead (voiding warranty) once to clean the dust under the buttons.