So, what to do? Take 'em apart, sure. But that's not always a simple task, and who wants to pry off and then re-glue the retaining ring of a Mighty Mouse? Many suggest using alcohol which is right on (though it wont get the waxes) but cotton swabs and the like are not enough.
Try this. I've done it and it works wonders. Use ethanol with as high a proof as you can find (e.g., 190 -- the lower the proof the more water, and some of that water is free). Perhaps test the mouse shell to make sure its not coated with some funky alcohol soluble coating first. Now, if you have enough alcohol, simply submerge the mouse for a minute or so -- yup, the whole thing. Otherwise, pour the alcohol into any openings or seams and use a lot. Gently swirl the alcohol around in the mouse for a minute or so and then drain it, shake it a bit, whatever.
Compressed air, even an aquarium air source, helps dry out any remaining liquid. So does simply waving the mouse through the air for a while. Alcohol evaporates quickly. Isopropyl works too, and in fact attacks some oils a bit better, but make sure you find the 90+ percent stuff. Standard rubbing alcohol is 70%, so 30% is water. Better solvents exist, but many attack plastics.
[robg adds: I haven't tried this one, but it sounds intriguing. I've been using a toothbrush on my Mighty Mouse's roller ball, and that's been working quite well. What are your favorite mouse cleaning techniques? And if anyone else has used this method, please post your experiences.]