Well, a Zombie is the most classic monster. They are dumb because they have no brain functions, only motor functions. In most zombie lore, a zombie has lost all of the things that make them 'human' due to a rotting brain and/or whatever method brought them back, but they retain human motor functions as long as their flesh holds out.
A skeleton has pretty much been reanimated by magic. Thus, they are given whatever skill set their creator (I'm assuming Dracula or some Devil Forgemaster) has imbued upon them. Because of this, they can be pretty smart. Also, since they are animated by magic, they do not have limitations like "I don't have tendons/ligaments, I should not be able to move at all without falling apart". Some kind of magic force keeps the bones together. Of course, if they are attacked and break apart far enough, Skeletons lose their power.
What is cool is that you can reinforce them with armor and give them a more powerful skill set. That's when you get Blade Masters and Mace Skeletons.
A mummy has an odd mythos. They have that whole "I used to be a powerful pharaoh in Egypt" thing going for them. They may very well have ancient magic going for them. Unfortunately, mummified corpses can barely move, so they, in turn, end up moving very slowly like a Zombie. However, because they were mummified with anointed bandaging and special oils, whatever magic they wield, I think, can be used to manipulate the bandages and harden them. When they throw their bandages at you, they're using magic to harden it as it flies past you... like knives.
Sucks that they cannot move much. I would bet they would be pretty powerful if they can move. Some have been known to teleport by unwrapping themselves and rearranging elsewhere (Akmodan the First, the boss of CV4's ClockTower).
Anyway, that's the way I see it.