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By Adam O
This idea is so simple that I'm certain I'm not the first to think of it, although I do not know of anyone else who has.

Fill a ring-shaped tub with water. On one side of the circular containter, place a propellor which is powered by a motor. This starts a current and circulates the water around the tub. On the other side of the containter, place another propellor, but this one is connected to a generator. The motion of the water turns this propellor, thus generating electricity. Wire the generator to the motor, and the generator supplies electricity to the motor which continues the flow of water, allowing the generator to continue to produce electricity, etc etc etc.

If this device worked, it would never stop moving. Ever. It is a perpetual motion machine, something that science has determined to be physically impossible. Obviously, the device could never work in practice, but in theory it seems to make perfect sense. Why doesn't it work?
By pretzels
Well, it's the same old story... it's the equivalent of connecting a motor and a generator by the same shaft and wiring them together.
It takes more power to run the motor and all the losses due to friction and inertia (mechanical and electrical -- and you can even throw in gravity) than the generator can produce while being driven by that motor. And that's the same principle that would stop the circular bathtub idea from working also -- losses due to friction and inertia. Our entire observable universe appears to have the same problem, that is, it is apparently running down. If you could tranfer energy without any loss whatsoever then perpetual motion would be a snap, but the transfer of energy in any form always comes with losses.

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