Here is the straight physics story as far as I know:
Energy cannot be created or destroyed by us, the sun or the cosmos, but only converted from one form to another. The conditions for the creation of energy no longer exist.
Edit: Energy can be converted one form to another, but there are always losses. Some converts into forms we cannot use.
Most energy on earth comes from the sun. Ultimately all of it comes from the big bang, even if via a tortuous path of interstellar events, the evolution of suns, their destruction, and so on. Small amounts reach the earth directly from events in the cosmos, even direct radiation from events shortly after the big bang, but this is so spread out it is hard to detect, never mind utilise. There is plenty of evidence to support these theories, which is why they are theories, not hypothesis.
Almost all the energy we use is free. It is available in large amounts by intercepting direct radiation from the sun and converting it to plants, rain, heat or electricity, etc. Other "free" sources include gravity, fossil fuels, bio-fuels, nuclear fuels, wind, geothermal and so on. The actual energy is available from or stored by some other process, meaning we get the energy for the cost of extracting or collecting it only. This compares with energy stored in a battery or reservoir, which had to be paid for first.
Free energy as you mean is not so clearly defined, but generally means something about an alternative or high tech or little understood resource that has no mainstream acceptance, leading to conspiracy theories about why this is not accepted, ridiculed etc. The second link has as good an appraisal as I have seen. Typically we see terms like over unity, perpetual motion machines, zero point energy etc mentioned or implied. The third link explains zero point energy, a mainstream concept from Einstein.
While there are plenty of descriptions of free energy devices around on the internet, often based on electromagnetic gizmos related to generators, and gravity devices like wonky pendulums, there is little (or is it none?) evidence that they really work. It shouldn't be so hard for someone to prove the operation if it really works. Instructions for others to build and test the machine are a first requirement, so that its operation can be replicated, understood and analysed. Replication is the test of any experiment. It is usually somewhere around this point that things become vague, and drift off into weird statements, conspiracy theories about power companies or big oil or such like. The proof is in the evidence. If it really works there are plenty like me for example that would accept that it was possible. So far it depends on a leap of faith, which I just don't have. Some systems are just scams, get rich quick schemes for the gullible. I am sure at least some of the purveyors of alternative machines are quite genuine, but perhaps believe too much in their device. The second link lists several of the well known ideas, and some are about generators. Basically this is a case of put up or shut up, otherwise it is just going on about the wisdom of ancients, lost knowledge, pseudo science, conspiracy, whatever. If there are no instructions then there is no machine. See the fourth link for interest. It does have instructions, but no-one has made a prototype that works it seems. Incidentally having a patent is no guarantee of reality.
Another thing to consider is that there are real alternative engines, generators, systems that work on proven principals, but do not get taken up because they are not competitive with existing machines. One example that did take up a little was the Wankel engine. Basically it is the consumer/market perspective as well as the manufacturers who are resistant to these kind of developments.
If there is something that really works it would soon be taken up and become mainstream. Also I am certain that its operation would soon be understood. The understanding of this kind of thing is high. Also, it is always possible that something is being missed, like an ability to steal something from another dimension, but these things are pure conjecture, no evidence whatever.
In the end I think a lot of it is to do with the great ability we have to take things on faith, love conspiracy theories, and want to believe the impossible is possible. This is the very essence of magic, as illusion or as we fantasise about.
A fertile but parallel field is the field of medical devices working on mysterious principals like zero energy, or transistors connected in unusual (meaningless) ways. This field is more likely to involve scams though. Then we have dowsing, crystals. These all show how much we want to believe in fantastical things.
The truth is that the universe and what we know as most likely true or almost certainly true are fantastic enough as they stand.