I find that the most appealing part of a superhero’s story is that concerning the character’s origin.
Take Superman, for example. Here you have a character who grows up knowing that he is different, that he can do all sorts of strange and cool stuff. However, he feels the need to fit in and so tries, as much as possible, to conform. It isn’t until later that he decides he wants to truly find out who he is, and embarks on a quest to find out.
To look at another famous origin story, there is Spiderman. In this, we have the geeky, teenage Peter Parker, who is already struggling to fit in, when he gets bitten by a radioactive spider (Or genetically enhanced spider, dependant on the version and era). Thereafter Parker finds that he has new purpose expressed through these wonderful new powers. He is no longer a nobody.
Just by looking at these two examples, it is very clear to see why the superhero genre is still popular, particularly with teenagers and, in particular, why origin stories keep getting re-told throughout the decades. These superheroes mirror the adolescent who struggles to find their place in society. In the first instance, the yearning of Clark Kent mirrors the teenage yearning to understand who we are, and what exactly our place is in the world. In the second instance, Peter Parker demonstrates the same thing, from a different perspective; he mirrors the feeling that most teenagers have, that they don’t fit in, but yearn for some indication of purpose and acceptance; something that is delivered to Parker in his spider accident.
In conclusion, we sympathise with the origin story because we all struggle to understand our place in the world, and we love being told these stories because they are pregnant with hope and promise that we may find the answer.
Although, unfortunately, that answer probably won’t involve awesome powers.