Has any permanent magnet motor been proven to run? I have read lots of articles about permanent magnet motors, some of which claim the possibility and other which refute it.  Is it possible to have a permanent magnet motor that runs on the magnetic force of permanent magnets?
 A: Magnetic field, and interactions of atoms with magnetic field, conserve energy, i.e. no net energy gets created at any point. There is not a lot of energy in the field of even a strong permanent magnet. One could, in principle, construct a 'motor' that would demagnetise the magnets somehow, converting the field energy into motion, but it wouldn't be some effective super energy storage or the like, and would run for some time then stop. 
I think the reason people turn to magnets when trying to build perpetual motion devices is that it is harder to understand energy conservation in this context, and furthermore it seems more magical. The fact is, the laws governing electromagnetic interactions are very well known, incorporate conservation of energy. There is the point of "what if the scientists are wrong?" Science, indeed can be wrong sometimes. But if this particular knowledge was off by more than utterly microscopic amount, the computer you use to read this message, the communication equipment, the power equipment, the generators, the hard drive in the computer storing this message, and so on, would not have been possible to engineer.
A: Why, here you go, an example of permanent magnet motor - a Curie engine.
Motors that combine permanent magnets and electromagnets are common too.
Thing is magnetic field as a means of storage of energy is subject of the same thermodynamics laws as the rest of the universe. If you want the motor to move, you must change the field. To change the field you must expend energy one way or another. Something like a motor that uses just permanent magnets with no external energy sources is impossible. Now ones that use permanent magnets and little more - like in the example, a heat source - these are common.
The linked engine uses the Curie effect - metals above certain temperature cease to be ferromagnetic - attracted by magnets. And while you could theoretically build such a motor in a way that restores spent heat energy, it will still need to spend more heat to remove ferromagnetic effect from a magnetized piece of metal than from unmagnetized one.
