In general, and in no particular order: Believable power scaling. Dragon Ball Z was just a game of one-uping without end. A tragic backstory for the sake of a tragic backstory doesn't mean anything. (maybe unpopular opinion) but action scenes are all well and good but without any sort of established stakes to tie it down just becomes meaningless filler. Avoid deus ex machinas How superheros effect the world on a day-to-day basis? Are there superhero schools/licenses? Are there government agencies after the superheros? Can superheroes get sponsorships from corporations, etc.
Give them weaknesses. Real weaknesses, not a stupid glowing rock. Overpowered heroes get boring (and annoying) really damn quick. Have them get their ass handed to them by someone with no powers who figured out how theirs work. Force your hero to develop skills so they don't just rely on their power(s). Try to come up with unique powers-Not just super speed, super strength, ect.
Here are some points I personally think we don't see enough in superhero stories: Have them gain control – slowly. Controlling super powers should be like training a (new) muscle. Is the character well suited for these powers? Not often enough do I see a wimpy character refuse to use, or slowly grow into the superhero role instead of being courageous from the get-go. Your main superhero doesn't necessarily have to be the strongest character. Perhaps the character has role models of his own. Give them limits. If you consider the super power a muscle, can it be strained? Damaged even?
Don't give your superhero a really dumb name (or power). See DC's Matter-Eater Lad and Arm-Fall-Off-Boy.
Don't make your superhero a perfect person in their "real life." Tony Stark is an alcoholic. Bruce Banner is terrified of becoming the Hulk because he can't control the Hulk. Dr. Manhattan is cold and uncaring. Remember that the difference between a superhero and a supervillain might just come down to the audience's point of view - where the director puts the camera, so to speak.
One man's terrorist is another's freedom fighter. Perspective matters. It would be interesting to see a superhero/supervillain story where the alternating chapters are telling events from each sides view, and at the end the audience is left to decide who is the hero and who is the villain.
If we're talking prose superhero fiction, I've noticed a tendency to focus on flashy elements--powers, fights, costumes, etc.--over character. Problem is, those flashy elements lose much of their punch in prose. So I'd say take advantage of the greatest strength of prose: how deep you can dig into characters.
