Interestingly (and slightly disturbingly), there is a "Real life superhero" movement:
In real life, of course, these people don't have powers, and are at best activists with a gimmick or glorified cosplayers, at worst small-time vigilante thugs with a gimmick, though its still an interesting subculture (I saw a documentary film on this phenomenon years ago when I was living in Toronto- I remember Stan Lee was interviewed in it, but I can't recall the title).A real-life superhero (RLSH) is a person who dresses up in a superhero costume or mask in order to perform community service such as neighborhood watch, or in some cases vigilantism.
Early examples of this type of behaviour are reported from the 1990s, e.g. with Mexico City's "Superbarrio", who in 1997 donned red tights and a red and yellow wrestler's mask in order to organize labour rallies, protest, and file petitions to prevent families from being evicted. A "real-life superhero community" in the sense of an online subculture began to develop in the mid-2000s.
Of course, in the real world, a superhero would be greatly limited in what they could accomplish, due to the absence of powers and the presence of functional law enforcement and organized crime syndicates far more powerful than any one non-powered individual. If they were to act within the law, they would basically be limited to activism or charity work with a colorful gimmick or limited neighborhood watch work/citizens' arrests, as noted above.
But I wonder if a full-blown superhero setting could emerge in the real world. What it would take, and what it would look like.
As I see it, it would require three things:
1. A culture which glorified individualism and specifically vigilantism, and in which superheroes are highly popular/a culture that values showmanship. The modern US has all of that (indeed, I would argue that superhero comics and their off-shoots are probably among the most uniquely and truly American forms of culture, at least in their original origins).
2. A breakdown of effective law-enforcement, and of public trust in law enforcement. The modern US is creeping more and more toward this, unfortunately.
3. A country without a level of armed, organized crime, or law enforcement, that would be impossible for individuals or small private groups to successfully confront. The modern United States most certainly does not fit this criteria. Indeed, it would be very hard to have the second criteria (essentially a failed state) while also having the third criteria- failed states tend to feature larger, well-armed terrorist/militia forces and/or organized criminal groups.
I suppose you could have a large militia of guys in costumes with automatic weapons, but that wouldn't really be a superhero setting in the sense that its usually understood.
What you would need, in short, would be a fairly peaceful, probably fairly small country without effective central government and with a culture that places a premium on individualism and showmanship. Has such a thing ever existed in the real world?
Also, what sort of "realistic" powers might occur? Not things that are flat-out impossible (either including or not including the possibility of further radical advances in cybernetics or genetic engineering), but on the high-end of the bell curve of human ability, physically or mentally? What sort of skills or innate abilities would be most useful for a real-life superhero? Alternatively, for a non-powered hero, what sort of equipment and training would be within the range of someone with an average income, as opposed to a Bruce Wayne or a Tony Stark?