Regarding myths, an incredible example is that of the Bible reference of the Sun stopping in the middle of the sky…
Velikovsky studied the reports in the Bible of the Sun coming to a halt in the sky. Many people dismiss this story as completely absurd. But yet again a scientist should investigate every possible solution, not only those which fit in his current worldview. So Velikovsky thought cleverly: If people in a point on Earth reported of a “long day” due to Sun stopping in the sky, in the OPPOSITE side of the Earth there would be people reporting a “long night”! Imagine what happened next: Velikovsky indeed discovered that people at America indeed had ancient traditions [Annals of Cuauhtitlan] which spoke of a large night! (and no, the fact that we do not know HOW this happened does not mean that it did not happen)
Velikovsky in general postulated not only that myths were not fairy tales (all serious thinkers understand this today) but that they should also be interpreted literally. So he tried to analyze many myths so as to find evidence of great cosmological events and disasters. His theories include explanations of the Biblical events of the Exodus, of the great Cataclysm, of the destruction of the Babel Tower and of the destruction of Sodom.
Despite his theories looking crazy, modern science has started to understand that the current standard cosmological model is not so valid as once thought. Thus it seems that there is space for the ideas of Velikovsky (which include some astounding verified predictions) which I will shortly present.
The views of Velikovsky – A summary
Velikovsky thought the solar system was a system which in its history experienced great changes and violent collisions. This may not sound like a novel idea today, but it was a very radical idea when Velikovsky presented it. Back then everyone believe that our solar system is during some billion years in a balance with no more violent cosmic events taking place. Comets were considered celestial bodies which were exiled to their weird orbits billions of years before. But Velikovsky thought otherwise: He spoke of a solar system which was still violent, changing, shifting. He spoke of world cosmic planetary collisions when other visualized a peaceful dark space. He even postulated that Venus was in fact a comet which was extracted from inside Zeus (Jupiter) very recently! Velikovsky also thought that electromagnetism was the most important force in the universe [Zeus and his thunders]. He talked about the Sun and how it was a charged celestial body (while others back then thought it was neutral) and how the universe was an “Electric Universe” (EU) with electrical fields in which all the celestial bodies move generating various phenomena we wrongly attribute to other causes. (he even thought the force of gravity should be revisited) The tail of the comets was also a result of such an electrical interaction.
The war. The verification.
In general the ideas of Velikovsky were so innovative that they were fought fiercely by the scientific establishment of his time. The war against him came to be known as "The Velikovsky Affair". The scientific establishment cannot listen to people from “outside”. And yet, the crazy ideas of Velikovsky are proven correct one by one over the years. He had predicted that Venus will be too hot on the surface because of its recent formation. He was proved right. [1-0] (Sagan tried to disprove him by stating that the Greenhouse Effect was the cause of the temperatures on the surface – but no climate model can explain these temperatures) He thought that the infamous Red Spot reaches up to the core of the planet and is the result of the creation of Venus from Jupiter. And it is true that from the recorded planetary orbits from the time of ancient Greece until today these orbits seem to be not entirely stable. Venus also seems to have a “tail” [source, source] like a comet, while modern simulations  have shown that such an event like the one Velikovsky postulated is not totally implausible. [2-0] Velikovsky also predicted that Jupiter emits radio waves. He was proved right. [3-0] (Sagan again tried to diminish the importance of the prediction by saying that it is now known that all bodies emit such waves – but after the coming of Christ everyone is a prophet) He predicted that the solar system is still violent. He was proved right. [4-0] We now know the collisions that Earth survived. We have witnesses a comet colliding with Jupiter at the same time while our astronomers imagined of the cold peaceful space. He predicted that the tail of the comets is not due to vaporizing water. Evidence seems to validate him.  He predicted that the comets are relatively newly formed objects. Again the current evidence from the comets we have examined (e.g. Rosetta Mission) seems to prove him right once again [5-0] since scientists discovered oxygen on them. (oxygen is reacting easily with almost everything, so if the comets are old how could this oxygen still exist?)  And his theories of an electrical universe sound even more plausible if one realizes that they could explain why the Sun is hotter on the outside than the inside...
In essence there is no prediction made by Velikovsky which was refuted. It was just that his ideas annoyed some narrow minded people who thought that their ego or their faith in a weird “holy” status quo  was more important than the advancement of science.
Instead of an epilogue, I will just quote what professor H. H. Hess [President of the American Geological Society/ Chairman of the Space Science Board] wrote to Velikovsky…
"We are philosophically miles apart because basically we do not accept each other's form of reasoning — logic. I am of course quite convinced of your sincerity and I also admire the vast fund of information which you have painstakingly acquired over the years.
I am not about to be converted to your form of reasoning though it certainly has had successes. You have after all predicted that Jupiter would be a source of radio noise, that Venus would have a high surface temperature, that the sun and bodies of the solar system would have large electrical charges and several other such predictions. Some of these predictions were said to be impossible when you made them. All of them were predicted long before proof that they were correct came to hand. Conversely I do not know of any specific prediction you made that has since been proven to be false. I suspect the merit lies in that you have a good basic background in the natural sciences and you are quite uninhibited by the prejudices and probability taboos which confine the thinking of most of us.
Whether you are right or wrong I believe you deserve a fair hearing." 
And only then will you really Know.
'Electric Comet' Could Burn The House Of Science (comets explanations)
Velikovsky's Ghost Returns (Electrical Sun + Electrical comets etc)
Ancient Destructions explained – Immanuel Velikovsky and the Electric Universe
Scientists support Velikovsky by DR C.J. RANSOM
Everything is Electric - Comets are not primordial
Everything is Electric - Planetary formation in an Electric Universe
Everything is Electric - Immanuel Velikovsky
The exploded planet hypothesis (+Planetary Explosion Mechanisms)
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