Superpowers? No, of course not. Any manner of super powered beings, from ancient mythological figures to aliens and ghosts and vampires and such, are not generally considered superheroes. And then we have "superheroes" like Batman, who are arguably defined in part by their lack of super-human powers (at least, beyond the normal implausibility of action heroes).
Heroics? Nope. Not only is the definition of "hero" obviously a hotly contested one, but their are many heroic characters, even super-powered heroic characters (see above) that are not regarded as superheroes.
Is it the iconic nature of the characters? Hell, is it the campy costumes?


Is it a particular set of genre conventions? I'm not sure. You can find authors who challenge a lot of these conventions, and a lot of these conventions (the sidekick, the secret identity, etc.) predate, or at any rate can be widely found outside of, the genre.
Is it that they act outside the law? No. The outlaw hero archetype long predates the modern concept of the superhero, of course.
Is it simply being a hero in a Marvel or DC publication?

So how does one define a "superhero"? It seems to be widely agreed upon that Superman was the first, but by what unwritten but widely agreed upon definition, for example, is Batman a superhero, but Sherlock Holmes and Robin Hood are not? Do you just have to check a certain percentage of the criteria to qualify?
Just for fun, I've tacked on a poll, with some examples to illustrate this conundrum. Four are famous characters who are widely regarded as superheroes, but who, to my knowledge, generally lack innate superhuman powers. Four are famous characters who are not widely considered superheroes, but arguably fit most or all of the criteria listed above. Two are grey area: Buffy is borderline because she drew inspiration from Marvel comics and is described as a superhero in the second episode by Xander, while Coulson is a hero in the Marvel universe, and an augmented one after he loses his arm, but is not generally described as a "superhero".