The superhero genre has been a remarkable literary/cultural phenomenon of the 20th century, conventionally traced to Segal & Schuster's invention of Superman in the late 1930s. However, the superhero wasn't entirely without precedent: Victorian and early 20th century fiction was full of crime-fighters, adventurers and villains with attributes such as particular costumes, special abilities and secret identities. Rather than try listing them, the easiest recomendation is to point to the The Wold Newton Universe, Philip José Farmer's lovely unifying conceit of the "Wold Newton Family". Its premise is that these outstanding fictional individuals - notably Sherlock Holmes, Tarzan and Doc Savage - are all related, their powers arising from mutations when the occupants of a carriage were exposed to radiation from the 1795 Wold Newton meteorite.
Nevertheless, the idea builds on mythic motifs going back as far as you like. M Night Shyamalan's film Unbreakable, which also analyses comic books, takes as its superhero definition one who has powers but a particular vulnerability. This fits Samson (super-strong as long as his hair isn't cut); Achilles and Siegfried (invulnerable except for one location), or Lleu Llaw Gyffes in the Mabinogion, who can't be killed
during the day or night, nor indoors or outdoors, neither riding nor walking, not clothed and not naked, nor by any weapon lawfully made
Like Samson, he makes the mistake of telling his lover how this can be circumvented. If you ignore the vulnerability part, there are many others: in Greek mythology the obvious one is the super-strong Herakles (who meets at least one super-villain, Antaeus), and in Celtic mythology, the warrior band of the Fianna contained individuals with unusual and idiosyncratic powers. Quite apart from the basic qualifications ...
the applicant would stand in a waist-deep hole armed with a shield while nine warriors threw spears at him; if he was wounded, he failed. In another his hair would be braided, and he would be pursued through the forest; he would fail if he was caught, if a branch cracked under his feet, or if the braids in his hair were disturbed. He would have to be able to leap over a branch the height of his forehead, pass under one as low as his knee, and pull a thorn from his foot without slowing down. He also needed to be a skilled poet
- Wikipedia, probably paraphrased from Celtic Myth and Legend, Charles Squire, 1905
... many of the Fianna had special powers: Diarmuid Ua Duibhne had a "love spot" on his forehead, which would make any woman who saw it fall in love with him; Caílte mac Rónáin could run remarkably fast and communicate with animals; and the leader, Fionn mac Cumhaill, had tasted the Salmon of Knowledge after burning his thumb while cooking it, and could access special knowledge and wisdom thereafter (I suppose the equivalent of Googling) by sucking on that thumb. Another hero from the same mythology, Cúchulainn, achieved immense powers in battle by a shape-changing frenzy that makes the Incredible Hulk look effete. In his battle frenzy, termed "warp spasm" by the translator Thomas Kinsella, Cúchulainn became:
a monstrous thing, hideous and shapeless, unheard of. His shanks and his joints, every knuckle and angle and organ from head to foot, shook like a tree in the flood or a reed in the stream. His body made a furious twist inside his skin, so that his feet and shins switched to the rear and his heels and calves switched to the front... On his head the temple-sinews stretched to the nape of his neck, each mighty, immense, measureless knob as big as the head of a month-old child... he sucked one eye so deep into his head that a wild crane couldn't probe it onto his cheek out of the depths of his skull; the other eye fell out along his cheek. His mouth weirdly distorted: his cheek peeled back from his jaws until the gullet appeared, his lungs and his liver flapped in his mouth and throat, his lower jaw struck the upper a lion-killing blow, and fiery flakes large as a ram's fleece reached his mouth from his throat... The hair of his head twisted like the tange of a red thornbush stuck in a gap; if a royal apple tree with all its kingly fruit were shaken above him, scarce an apple would reach the ground but each would be spiked on a bristle of his hair as it stood up on his scalp with rage.
- The Táin, trans. Thomas Kinsella, Oxford University Press, 1969
There are similar examples - see Google Books - in The Epic Hero (Dean A Miller, JHU Press, 2002, ISBN 0801862396) which looks generally worth finding for its exhaustive survey of the characteristics of the epic hero (a deal of it is previewable via Google). Miller devotes considerable space to the many attempts by commentators - JG Frazer, FR Somerset (Lord Raglan), RB Onians, and Joseph Campbell - to fit into a common framework the often very similar life scripts of epic heroes. Judging by the Campbell section from The Epic Hero shows, Miller doesn't appear to much like Campbell's work, especially later when he turned very Jungian and New Age; nor is Miller the only critic (more later). Nevertheless, Campbell's analysis of hero myth is probably the most celebrated and popularly known.
Campbell's iconic work is The Hero with a Thousand Faces, which proposes a "monomyth", a single heroic story (commonly called the "Campbell Cycle"). In its simplest form, it can be summarised as
A hero ventures forth from the world of common day into a region of supernatural wonder: fabulous forces are there encountered and a decisive victory is won: the hero comes back from this mysterious adventure with the power to bestow boons on his fellow man
There are various text descriptions that describe it in more detail; Wikipedia's Monomyth page summarises it pretty well. The applicability as a storyline to a number of classic heroes such as Herakles and Gilgamesh (including major religious figures such as Moses and Jesus Christ) is pretty clear. Jesus, Herakles and Moses, for instance, all suffer threats on their lives in babyhood. There's a bit of a wimpy tendency for modern expositions to tone it down by removing the final fall from grace and death of the hero (with this final quadrant included, the monomyth looks like an allegory of the human life-span).
Many works of fiction draw on the concept; I first ran into it in John Barth's Chimera, a self-conscious exploration of mythic storytelling which interweaves the tales of Dunyazade (sister of Scheherazade), Perseus and Bellerophon (the above diagram comes from that book). MK Joseph's The Hole in the Zero has a segment explicitly showing the cyclic nature of a Campbell myth. In that segment, Paradine becomes such a hero, but finds himself in a book:
"Lord Paradine is, in fact, a typical example of the kind of heroic superman almost invariably invented in cultures undergoing a final period of steep decline, as compensation for the experience of cultural overthrow. They are then normally taken over and elaborated in the romance cycles of the succeeding culture".
How accepted an observation this is, I don't know, but it certainly fits King Arthur (suggested by some to be based on a chieftain holding out against the Saxons in the Sub-Roman period) and Robin Hood (a mythical Saxon guerilla in an England long since taken over by the Normans).
However, the Campbell Cycle has acquired a particular foothold in cinema.
Movie and other myths
The best-known cinematic connection is with Star Wars, who was a fan and friend of Campbell, which led to a great deal of synergy: see, for instance, The Power of Myth, in which Bill Moyers interviewed Campbell at Lucas' Skywalker Ranch; and The Mythology of Star Wars with George Lucas and Bill Moyers. How much the Campbell monomyth shaped the original Star Wars trilogy isn't entirely clear; some critics have spotted that Lucas didn't begin talking about Campbell motifs until after their completion, even suggesting a degree of retrofitting. For example, Steven Hart - Galactic gasbag, Salon - finds more credible roots in pulp SF, and Lucas himself acknowledged influence from Kurosawa's The Hidden Fortress.
Campbell-spotting has become a bit of a hobby among movie buffs - The Matrix is another that's applicable with little effort - but it can be hard to separate stories that use a monomyth framework by happenstance from those that rework older heroic stories already following that framework, and those that use it by conscious choice (especially as Christopher Vogler's The Writer's Journey is standard reading for screenwriting courses).
Another director interested in the Campbell and myth is George Miller, and this manifested particularly in his post-apocalyptic Mad Max trilogy. These films, particularly Beyond Thunderdome, are full of standard mythic motifs - acquiring of helpers, puzzles and perils, and tricksters. The point where Max awakes from a coma to emerge from a cave in an idyllic gorge called Crack-in-the-Earth is about as blatant a figurative rebirth as you can get. Heroic Apocalypse: Mad Max, Mythology and the Millennium (Mick Broderick, orig. in Chris Sharrett (ed), Crisis Cinema: The Apocalyptic Idea in Postmodern Narrative Film, Maissoneuvre Press, Washington DC, 1993, pp. 250-272) is a detailed analysis in Campbellian terms; and there's more at Transparency Now's Mad Max Beyond Thunderdome: Salvaging the Future. (A couple of bits of Mad Max connection trivia: 1) the uncredited RiddleyWalkerisms in the "doing the tell" segment; 2) Paul A Cantor's lovely description of the works of Odd Nerdrum - such as The Water Protectors - as "the result if Rembrandt had painted the sets of The Road Warrior").
I don't 100% buy the Campbell interpretation of Mad Max. Even taking the whole trilogy together, in many ways Max doesn't fit the model of the Campbell hero. He doesn't particularly go on a quest. There is, arguably, a general theme of his personal development (from driven avenger toward altruism), but mostly he turns up out of the wilderness for routine aims such as finding fuel or recovering stolen property, eventually grudgingly facilitates the rescue of others, then departs back into the wilderness. In fact he is a character more in the mould of the "Man with No Name" style of hero whose story runs:
A community in a harmonious paradise is threatened by evil; normal institutions fail to contend with this threat; a selfless superhero emerges to renounce temptations and carry out the redemptive task; aided by fate, his decisive victory restores the community to its paradisiacal condition; the superhero then recedes into obscurity.
This is not Campbell at all, but the "American Monomyth" postulated by the theologian Robert Jewett and the philosopher John Shelton Lawrence in their books beginning with the 1977 The American Monomyth. For the basics, see this Dialogic Interview with John Shelton Lawrence and this Humanist reviewof The Myth of the American Superhero. Jewett and Lawrence argue that American storytelling, particularly within modern cinema, focuses on an essentially antidemocratic monomyth involving a hero wading in to alter a society that isn't working. They argue further that this even flavours US social policy (paradoxically, in a society for which collective democracy is supposed to be a core ideal; the same phenomenon as noticed by revisionist historian Ray Raphael - see July 4th and invented traditions - who is also concerned at the USA's perception of its past in terms of superhuman figures).
There is, then, a dark side to heroic myth, and that's one of the aspects that appeals about Watchmen. It's not just about darkness for its own sake; there has been a drift toward darker treatments of superheroes, but movies (as in the latest Dark Knight interpretation of Batman) still lean toward an implicit "end justifies the means" conclusion. Watchmen, at least in the book, uses darkness in a way that subverts the genre; some of its nominal heroes are intrinsically toxic (the Comedian, for instance, shoots his pregnant mistress, attempts to rape a fellow crimefighter, and throughly enjoys napalming the enemy in Vietnam) - something that as Zach Snyder says would never be countenanced in mainstream superhero movies that are linked to corporate franchises.
It comes down to world-view. Generally the superhero world is one in which these powerful individuals are presented as trustworthy to make decisions on humanity's behalf, and Moore's Watchmen runs counter to that. The Tides of History: Alan Moore's Historiographic Vision explores his stance in detail; it argues that, unfortunately, the comics industry didn't grasp his intentions and took Watchmen merely as precedent to "transform superheroes into violent, amoral killers". The essay is at ImageTexT, "a peer-reviewed, open access journal dedicated to the interdisciplinary study of comics and related media", which looks likely to repay further exploration.
Addendum: I forget to mention that it was Talk Like a Pirate Day on September 19th - which reminds me of one of the premises of Watchmen. In its world where costumed crimefighters actually exist, comic genres had taken a different turn and focused instead on lurid pirate stories. Tales of the Black Freighter at The Boredom Festival has stripped out the extraneous main story to reconstruct Marooned, the counterpointed pirate comic within Watchmen, about a shipwrecked mariner undergoing a horrific journey to warn his home town. ("The Black Freighter" alludes to Seeräuber Jenny from Die Dreigroschenoper).