Many of us can name several superheroes, and even talk about their origin stories, even if the person speaking is not an avid fan. We almost seem to be fascinated--but why?
Superheroes are as diverse as they are colorful, just like the everyday people in the pages of the comics and the frames of the films. Peter Parker deals with almost constant guilt. Uncle Ben dying, his Aunt May being sick because of his radioactive blood, Gwen Stacy dying as the result as a fight with the Green Goblin... he's got more than a few problems. We almost have heroes like Batman, who dwell in the shadow and is constantly dealing with the underbelly of Gotham City that many of its citizens almost seem to try and ignore. Superman has amazing powers, but even he struggles to keep his two lives separate.
We like to see elements of ourselves in superheroes. We like seeing them struggle because we sympathize, and then we as an audience are even more excited when the hero triumphs over the villain and saves the day. As a rule of thumb, we as a race tend to be fairly competitive. We like winning, and adding on the fact that the superhero fights for what he/she believes is right just us even more hooked. We like when the good guys win and there is some peace, even if it's only temporary.
We like superheroes with flaws. Part of the reason Marvel has done so well is that they have an uncanny ability to give their heroes a struggling side. Tony Stark struggles with alcoholism, as a well known example. He does not have to be a hero to struggle with this, but it adds another dynamic to his character and it impacts his relationships as well, particularly with a Miss Pepper Potts. But we love him anyway. We love his struggle and the fact that he wants to be a good person, despite the things he has done in the past or what's happened with his past relationships.
People are complex, and we want superheroes to be complex as well. We want them to deal with war, death, and heartbreak. We kill those who are supposed to be immortal, and then bring them back to continue their tale. We want writers to create complex characters, not just with superheroes, but with films, books, video games... the list goes on.
The Superhero can be a role model. A comfort. An escape, even if just for a short time. We experience love, loss, pain, and growth with them, and we grow to love them, regardless of how outlandish the stories may seem.