Less conventional superheroes

Daredevil

Disabled because he is blind. He can 'see' through hearing sound bouncing off surfaces.

Hancock

Alcoholic. Anger issues. Careless. Black. Homeless.
The film is about him getting on the right track again to become a proper superhero. He even gets a superhero costumes towards the end.

These both have films all about them and are successful eventhough they are your regular heroes. However as Hancock is a comedy this helps it be successful as it makes people laugh.