How about Led Zeppelin as a rocking super-group. Tons of charisma, and super-sonic powers. Jimmy Page blasting out killer riffs on his magical guitar that is actually “The Hammer of the Gods”, Bonzo with the mystic drumsticks, Jones with the bass that triumphs over evil, and Plant with vocal blasts sorta like Marvel’s Dazzler–but cool.
Or Jimi Hendrix…similar to Page with the uber-guitar, with maybe a 1% chance of sucessfully casting “Summon Cylon” by accident…
Bettie Page, famous 50s pin-up model, posed in several “jungle girl” outfits. Perhaps wild animal based powers?
A “Jack, the Giant Killer”-type figure?
Johnny Appleseed.
His power–control over plants.
The whole apple-advocate thing was to distract people from his other horticultural adventures.
Cyrano de Bergerac. The guy really was a phenomenal swordsman. And, what if he really did travel to the Moon? (In his story about that, he described a hot air balloon about a century before anybody bothered making one; and several other methods, eventually using rockets.)
You weren’t thinking of this little gem, were you? KISS Meets the Phantom of the Park 
Karl Friedrich Hieronymus, Freiherr von Münchhausen
Count Alessandro di Cagliostro
Thomas Edison, Nikola Tesla, Albert Einstein, Werner von Braun, Eli Whitney, Thomas Jefferson, and Benjamin Franklin were all members of the American branch of the Hermetic Order of the Golden Dawn. They used the money from their inventions to finance more . . . . exotic . . . . experiments.
Alexander the Great.
The story goes that his father found his mother having sex with a snake. It’s icky until you realize that the great god Zeus often took the form of a snake.
His father even asked an oracle if the child which was born 9 months after this was his of Zeus’s. The oracle implied that Alexander was the son of zeus.
Alexander himself was obsessed with the question and visited several oracles and they all answered that he was half god.
Super Alexander!
Prince Vseslav of Polotsk. He was alleged to have been born of a witch, and to have been a werewolf!
Adolphe Sax, inventor of the saxophone and several other wind instruments, may have been the most accident-prone youngster of the first millennium. He was poisoned, burned, fell in a river and (later) out a 3rd floor window, and several times was almost gassed by the varnish on pieces of clarinets and bassoons that he’d left in his room to dry overnight.
As if that wasn’t enough, he survived at least one assassination attempt by a competitor who couldn’t match his action, and at age fifty-something was somehow cured of a particularly loathsome-sounding oral cancer by a mysterious Indian healer. Despite all this, and being blackballed out of the music industry by jealous rivals, he survived in good shape till the age of 80.
His daily breakfast comprised steak, eggs, and a bottle of Bordeaux. This alone might have killed off a lesser constitution.
Adolphe Sax: the Chuck Norris of music. Appreciate the man.
If somebody who’s conquered a good chunk of the civilized world asks you if he’s a god, you say “yes.”
How about Nostradamus? Major precognitive abilities.
What about the Mercury Seven?
* M. Scott Carpenter (1925 - )
* L. Gordon Cooper, Jr (1927 - 2004)
* John H. Glenn, Jr (1921 - )
* Virgil I. Grissom (1926 - 1967)
* Walter M. Schirra (1923 - 2007)
* Alan B. Shepard, Jr (1923 - 1998)
* Donald K. Slayton (1924-1993)
Astronauts are primary candidates for gaining superpowers.
Or being turned into Atomic Monsters, take your pick.
I was originally gonna go with King Canute, but I think instead a better pick (with minimal impact to your story) would be his father, Sweyn Forkbeard.
See, Forkbeard could control the tides, allowing his longboats to land at will rather than waiting for the tide.
Poor Canute thought it was perfectly normal, and that all the Kings could do it. Thus, when he becomes King, legendary history is made…
Damnit…I was going to suggest Peter Francisco.
Anyway…
Blackbeard. According to legend, after his final battle (where he was shot five times and stabbed more than twenty…before being decapitated), his headless body swam around the ship a few times before “dying.” Clearly, some kind of crazed immortal or regenerator.
Not human, but the Beast(s) of Gevaudan.
Prob’ly more, later.
As promised…Jack Churchill. He was…well, just read it.
Jasper Maskelyne. A good deal of the technical illusions he created were obviously a cover for the use of real powers…the ultimate misdirection.
The Mad Gasser of Mattoon. If he was actually a man at all, in the end.
Rabbi Loew, known experimental ceramics enthusiast.
Francis of Assisi, can psychically control animals (e.g. the wolf of Gubbio)
not-medieval, but a character similar to Rasputin would be “magician” / swindler Cagliostro ( Alessandro Cagliostro - Wikipedia ). In the Alexandre Dumas novels he is presented as an immortal who can predict the future and can hypnotise people to make them do his bidding.
Amelia Earhart was able to travel to other dimensions. Unfortunately, she lacked the ability to travel back.
My first thought was the SNL classic question:
What if Eleanor Roosevelt could fly?
Gandhi,
He took on a superpower; used no known physical weapons; and directed millions of persons with his mind, words, and deeds.
King Kamehameha, unified Hawaii as a brilliant general and threw a spear through a mountain.
Audie Murphy. The man knows killin’. Super reflexes “bullet time”, or danger sense?
Uri Gellar, hey, he really could bend spoons.
Doug Henning, faked his own death.
MC Escher, can draw paintings that you can enter and the doors lead to different places.
Some generic faith healers might actually have power.
James Randi has the ability to damp other’s abilities.
Jack of All Trades, somebody with intuitive aptitude, i.e. immediate mastery of a virtually limitless array of skills? Could have started out as a gentleman criminal, the master thief turned government agent by necessity sort (either was captured or decided to collaborate because of uncovering some Unknown Threat).
Jack Beanstalk, who has the ability of controlling plants? Can’t think of any possible backstory here, though.
You could perhaps also include some people who actually possess seemingly superhuman abilities, like those on this list, or maybe savants like Kim Peek, citing them as examples of ‘lesser’ power manifestations…