Superhero Archetypes
In the superhero genre, there are certain character archetypes that pop up more than others. TV Tropes can call these superhero expies. These are more based on their powers and skills rather than their personalities; as the powers can change and even be played with. Be advised that race and nationality will not be included in this essay.
The Paradigm (a.k.a. Look Below)
One major example is The Brick, as in the character who possesses enhanced physical abilities while occasionally additional powers including but not limited to flight, vision powers, and some form of energy control. One of the most famous is The Cape archetype with the poster boy being Superman. A variation of this is the feminine version I will call the The Amazon. Obviously the poster person for this is Wonder Woman.
Occasionally some of these characters have mythic roots like Wonder Woman and Thor, let's dub these Godlings.
The Olympics for Supers
Other Bricks include what I like to call Bruisers, characters with enhancements focus more on the strength aspect such as the Incredible Hulk or the Thing. Besides strength there are Speedsters like the Flash who can move at very high speeds.
Then there are characters that best suit different terrains with Flyers like Falcon taking the sky; while Amphibians like Aquaman feel at home in water.
What About the Non-Powers?
Fighters are a group of archetypes more closely associated with real life humans. These include Martial Artists like Iron Fist who use only their martial arts skills and only traditional weapons; although fictional elements like Chi often intertwines with it. Weapon Masters use weapons more often than their fighting skills and further divide by specialties. These include Archers like Green Arrow and Hawkeye; Swordsmen like Katana; and Gunmen like the Punisher (sometimes cowboys come up now and again). Acrobats use their agility and light weaponry in battle, famous examples being Daredevil and Nightwing.
Other fighter types include the Barbarian who often wield large swords. Jungle People are hardcore survivors like the classic Tarzan and Ka-zar. Assassins both old (Lady Shiva) and new (Winter Soldier) are another variant. Soldiers are people with highly advanced training; either that or enhancements with some type of super science like Captain America and Valiant's Bloodshot. Gadgeteers are users of portable and concealable equipment including Batman; unlike Arsenals who use loads of equipment on the fly. Spies like the Black Widow specialize in espionage and sabotage. Another thing of note is the Detective who either solve things with smarts, wits, and a few gadgets and powers.
Make Magic
Mystics are another offshoot of regular humans with special powers; this one being versed in magic or power that cannot be explained by modern science with characters like Dr. Fate and Dr. Strange being the epicenter of this archetype. Like martial arts though, the magic goes between hard and soft disciplines. This means chanting or conjuring spells without many requirements in the soft department. The hard disciplines however have more restrictions, many of which make use of artifacts.
Similar to magic, there are Psychics people with telekinetic and telepathic powers such as Jean Grey; and the occasional group of psychics like the Harbingers. Demonics meanwhile are beings that have gained terrifying power that are usually derived from taboos like Spawn.
The Latest Model
Science Heroes are all tech; and visually appealing science conventions with legs that show off their power for all to see.
The Machine groups deal more in technology including but not limited to giant robots. Armors are users of powerful suits that protect the wearer and enhanced physical capability while adding firepower and other features. Famous examples include Iron Man, X-O Manowar, and the Jaime Reyes Blue Beetle. Cyborgs are characters who have received enhancements and other features from bionic implants. Finally there are androids who are able to possess an intelligence bordering on a human.
Size Changers are another archetype that will have a highlight by a certain Marvel character. Size changing includes shrinking like the Atom or growing to gigantic size like Giant Man. How that affects the user depends on the writer and how the equipment plays out.
Energy users can control certain types of energy light or even the elements. Although most of the time it is usually just blasts like lasers or electricity. Occasionally they can shape them into objects like the Green Lanterns.
Is this Considered Mimicry or Physiology?
Animal is another distinct group. These include Beastmen who have traits or similarities between different animals or can even turn into them. The last bit are Shapeshifters and some can even turn into more than just different animals. Mimicry describes characters who have equipment and powers based on an animal like Spider-Man.
Miscellaneous Groups
Finally there are groups that are just that, groups. Secret Societies gather like minded people who face similar problems in the outside world like the X-Men. Organization Teams that are form as a task force like the Justice League and Avengers. Finally there are Families, groups of characters who share similar origins, powers, and relationships with others including the Batman family.
While there are other powers to consider like heightened intelligence with Living Calculators seeing the world as numbers and equations and Big Heads who have a higher intelligence and possibly other mental powers; these are the most common and there are probably other ideas out there that have not really caught on.