Problems such as bad interlock switches or a misaligned door are common culprits for microwaves that stop working. When these problems occur, they can cause a fuse to blow, stopping your appliance dead in its tracks. Replacing the fuse should get you back in the business of burning popcorn. If the new fuse blows in short order, your problem might not be so simple.
If your home experiences a power surge during a storm, it can fry the wiring of your microwave. The same thing can happen to an old microwave from plain overuse. Consider it death at an old age by natural causes.
Keeping your microwave clean is important to ensuring the appliance remains a long-functioning. Buildup of food deposits can cause sparks and overheating, leading to damage to important parts of the microwave such as the waveguide cove and the magnet core.