Regenerative/Healing Powers
You can be as strong and intelligent as you like, but without regenerative or healing powers, you will still have many bad days at the superhero office. Outside of alien beings (Superman, Supergirl) and mutants (The X Men), this particular power is closely associated with those characters that have experienced some kind of chemical interference with their natural state, such as Hulk, Deadpool and Swamp Thing.
It is also closely linked with invulnerability, which can manifest in a general way, or as a resistance to a specific threat. Green Lantern, for example, benefits from general invulnerability while wearing a magical ring, while The Mask is generally invulnerable with his facial accessory attached. Hellboy, on the other, giant, hand, is invulnerable to fire, while Blade is invulnerable to vampire bites.
This clutch of powers impacts upon the narrative of these characters, as the nature of the threats they face tend to be specifically tailored for their particular skill-sets. Superheroes with regenerative, healing powers, or invulnerability of any kind are far more likely to become embroiled in giant action set-pieces which push the boundaries set for less enhanced characters. This is because such heroes bring with them a certain level of comfort and reassurance – the audience knows they are likely to survive – so the story must increase the peril in order to create the necessary drama.