Leaving to one side the discussion of bomb-riding in Dr Strangelove (itself a blatant rip-off of the novel Fail-Safe, which was filmed simultaneously as a perfectly serious and rather good low-budget thriller by Sidney Lumet) and getting back on topic, it's a matter of record that Superman owed a great deal to Doc Savage, "The Man Of Bronze", who had a Fortress Of Solitude in the Antarctic and whose first name was Clark. Batman was inspired by, amongst others, the Shadow, Sherlock Holmes, and the villain in the film of a novel by the at the time very popular writer Mary Roberts Reinhardt called The Bat Whispers. And of course Zorro, a super-athletic champion of justice with a cape and a mask who pretends to be an ineffectual rich playboy and keeps his horse and other equipment in a secret cave under his mansion. Particularly the movie version of the character, played by the incredibly agile Douglas Fairbanks Sr. In some retellings of the Batman origin story, that's the movie the Wayne family are on their way home from seeing when they run into Joe Chill.
Also, a few years before Batman came along, there was a bad guy who appeared in Weird Tales a few times called Doctor Satan. If you can find the issue with the cover painting of him, he's wearing Batman's costume except that it's red. I've never heard him mentioned as a direct influence, but that image must have been visible on quite a few news-stands in the mid-thirties, and the very first preliminary sketches of Batman gave him a red costume - just saying... And of course the Joker's appearance was directly lifted from Conrad Veidt's character in The Man Who Laughs.
The Incredible Hulk was, as Stan Lee has said, originally based on Dr. Jekyll And Mister Hyde and Frankenstein (the Hulk was meant to have grey skin to make him look Frankenstein-ish, but it was changed to green in the second issue for technical reasons - apparently with four-colour printing it was really hard to print large areas of grey). And maybe he owed a certain amount to Heracles, a super-strong man of semi-divine parentage who, in the original story, was cursed with severe anger-management issues, and had to perform his most famous feats, some of which were forced upon him simply because they were ludicrously difficult, though some were genuinely useful, as a penance for "Hercing out" and murdering his entire family. And along the way he dealt with quite a few extremely specific serial killers who wouldn't have been out of place as Batman villains, including a guy who was obsessed with making guests exactly the same length as his spare bed, even if it meant stretching or trimming them, and another
fellow who had somehow trained a herd of horses to eat people. He even had a recurring supervillain - the goddess Hera.
Alas, not every Greek hero could have Zeus for a father, but never mind - even if you were 100% mortal, the gods might favour you with special equipment, usually forged by Haphaestus (who also built Talos, the loser in the first ever superhero team vs. giant robot showdown). Indestructible armour, swords that cut anything, helmets of invisibility - the works! As used by Perseus. So already we've got the classic superhero dichotomy between heroes who are innately gifted because they're more than human, and those who are mere humans but own unique special equipment, usually of magical or extraterrestrial origin.
And of course there was Achilles, a classic superhero who, thanks to exposure to what in those days had to be a magic river, but would in the comics inevitably have been a radioactive meteorite, had impenetrable skin - except in one place, because superheroes are no fun without a weakness. Though if Homer's Iliad is anything to go by, he was a retarded gay psychopath, so maybe he wasn't quite the traditional superhero after all... Then again, Troy might have been a far better movie if Brad Pitt had played him like that! And what about Jason and the Argonauts - the first-ever superhero team? There were even a few over-specialised characters included to allow "Aquaman manages to be useful" subplots. And a special guest appearance by Heracles, who left very early in the tale because it wasn't really about him, but he had to be in it somewhere.
For thousands of years, heroes, real or imagined, have been assumed to be "super" in some way, often by virtue of looking human but secretly being something else, just like Superman. Of course, if you don't have the cultural concept of life on other planets, then instead of being extraterrestrial, your heroes have to be at least semi-divine. About 2,000 years ago, a whole raft of people ranging from Buddha to Alexander the Great were popularly supposed to have been born of virgins, the logic being that if your mother had never slept with a human, then your father must have been a god, and if you make a great impact on the world, then obviously your father was a god, therefore your mother must have been a virgin (which is the reason the Virgin Birth story was worked into the New Testament). Some of the later statues of Alexander even take it for granted that he had horns! As for supervillains, them too - Attila the Hun (who, incidentally, was a dwarf) was known as "The Scourge Of God" by Christians, who assumed that anyone that unstoppable must be a supernatural being sent by God as a punishment to Christendom for not being Christian enough.
Even Robin Hood seems to have been a superhero in the true sense of the word. In Dark Ages England, the common people would have been afraid to wear green, since it was the colour of the fairies, who were taken very seriously indeed back then. Robin, along with Jack, is a very old generic name for male supernatural beings such as Robin Goodfellow, so somebody called Robin who wears the clothing of the fairies, lives in the woods just like them, and is incredibly good with a bow, the fairies' traditional weapon, has a distinct whiff of the supernatural about him. Indeed, way back then, a strange hooded man dressed as a fairy would have been at least as frightening to people who had reason to be scared of him as Batman would have been if he'd actually existed. "Tax-gatherers are a superstitious, cowardly lot - I need a costume that will strike fear into their hearts... That's it! I shall become a fairy!" How times change!
