To use your own examples (hydroplants and waterfalls), have you considered that these only work until the water source dries up?
"But," you object, "most of these sources don't dry up."
They don't dry up because the water is being replaced in some fashion, and performing that replacement requires energy. You would have to be heavily into math and physics to run the numbers, but the overall gain in the energy generated is ultimately going to be cancelled out by the amount of energy expended in putting more water back at the source.
The energy expended also, BTW, includes that which is lost through friction in the operation of the generating machinery, so the amount of energy that must be used in replentishing the source is always going to be more than the energy that is produced at the generator's "Out" port. The amount of energy available for consumption, measured against the energy diverted by friction of the internal components, is how a machine's efficiency is measured. Friction is also the main cause of machinery wear and tear.
So, in order for Free Energy to work, it must generate enough power to run itself plus some other machine, while consuming no fuel. It should also, ideally, be frictionless so that no energy is lost and the internal parts will never need replacement (thus requiring an outside energy source to perform repairs); this, in turn, requires either no wiring (electricity is subject to friction, which is how we get heat from electricity), or a perfect conductor which, so far, has not been found to exist.
In all cases, the concept is pretty simple: Energy requires fuel, fuel must be replentished, replentishment requires energy. And here's a rule that's fairly safe to follow: If you can't see the replentishment in a particular system, you're not thinking about it hard enough.