I am confused as to what you really mean by superheroes, so I assume that you don't really mean the fictional superhero. Anyone can be a superhero, as long as they have people who look up to them with admiration, love and respect. A hero does heroic things, and it does not have to be epic and otherworldly, it just has to be a deed that brings about good change and alleviates the suffering of another.
If you mean someone who donates to charity, does good stuff for random people and is overall a good person then yes (personally I believe no - but I'll come to that later). Of course, if that person has to save masses upon masses of people, cause incredible amounts of collateral damage to cities and basically be handsome/beautiful and hot, then no.
As for my earlier statement - yes, everyone can TRY to be a 'hero' but not everyone can be one. For one, you have to have a kind heart, a good soul and a respectable amount of money in your pocket. If you dont have that, you cant really make a difference.
Yes, people who are kind exist - but few of them have the time or money to be a 'hero'
Even if you don't take superhero as the definition of a hero with supernatural powers (in which case, they're just a hero), there's still the problem of legality.
Vigilantism is illegal and unlike the movies, I suspect it wouldn't be a simple case of concealing your identity and outwitting a bunch of amazingly patient cops who lack aim... It would get to a point where the government starts throwing that scary T word around (terrorist) and the police would be shooting on sight.
Also, being that this IS the real world and not a movie, no one would trust or respect some guy in a silly suit. No one would believe he was anything more than just another person and wouldn't be considered worthy of any respect - otherwise, everyone would be going out and trying to be superhero's (because apparently life is so dull without a movie script).