My microwave is used mainly to heat up left overs and the obligatory baked beans, somehow I always manage to buy exploding beans which just love to plaster themselves all over the insides. So the easiest way I've found to clean the grime is to use lemon juice, and very, very little elbow grease.
BEFORE: a very embarrassing picture of the inside ceiling of my microwave.
AFTER: all I did was one quick wipe to demonstrate how easy removing the splatters is,
of course you can take more time to get it uber clean.