Superman would probably be the most famous and popular superhero of all-time. I guess because we are all so familiar with him, Superman's powers don't seem very strange at all. He could fly (interestingly though, in the original Superman comics, he could not fly. He was a leaper. He would make giant leaps around Metropolis). In the Superman radio serial, he could walk through walls and even split himself into two Supermen.
In the 1980 movie Superman II, Superman had a power he never used before or since. He wiped out Lois Lane's memory of his secret identity- with a kiss.
Also, in one comic only (1947's Superman #45), Superman could merge himself with the wall (to escape from an alien prison). In this same unique comic, he molded his face to look like one of the aliens and convinced them to go home. He actually could manipulate the muscles in his face and entire body to assume a new form, in this case a yellow-skinned alien- with pointy ears and no hair, no less.
In another unusual and unique Superman (Action Comics #454) the Man of Steel had an unquenchable appetite. Superman usually is said to not need food because he gets his energy from the sun, but in this issue he scarfs down a mountainous plate of hamburgers.
Superman also once had the power of ventriloquism. In several 50's and '60's comics, the man of steel throws his voice around like Edgar Bergen. As far as having versatility in his super powers, I think we have to agree that Superman wins first prize, but let's move on.
Since the 1940s "Captain Marvel" has had seven different incarnations. Possibly the most unusual was the one from 1966, when he was actually a robot. He had detachable body parts. His head, arms, legs all would come off and could be fastened back on after serving a purpose.
"Black Bolt" had a great set of lungs, which caused destruction with his "quasi-sonic" scream. Even the faintest whisper of Black Bolt could wreck a place. He spoke only when he wanted to destroy things. This soft-spoken hero lived with his wife, Medusa, in a kingdom he ruled. Black Bolt was every woman's dream- a husband who won't talk back.
"Matter-Eater Lad" could eat matter (hence, the name!) His finest moment came when he stopped an indestructible machine from destroying the universe- by eating it. Matter-Eater Lad came from the planet of Bismoll (probably a pun on Pepto-Bismol).
"Bouncing Boy" bounced like a ball. "Chlorophyll Kid" had the power to make plants grow faster.
And how about "Arm Fall Off Boy?" Arm Fall Off Boy had an arm that he could detach (either arm), then he would use the arm as a club to hit villains with. Arm Fall Off Boy was a short-lived character from the 30th century.
"Dogwelder" is another definite contender. He had the power to levitate dogs and weld them to villain's faces. "Dream Girl" could tell the future through dreams.
In recent years, Marvel Comics gave us two more interesting women superheroes. "Princess Python" was an exotic snake charmer who had a trained a rock python who would attack on her command. And "Pretty Persuasions" takes the cake. Pretty Persuasions was the superhero identity of exotic dancer Heidi Franklin. She had the power to affect the sexual drives of others. (And couldn't we all have used her at one time or another in our lives?)
But possibly the oddest powers of any superhero were possessed by "Miss America." In the 1940's guy superheroes were all the rage, but a few super-women found their way into the comic books too.
In Quality's Military Comics (1941), a young, pretty reporter named Joan Dale made her debut. In the comic, Joan visited the Statue of Liberty. Gazing, she wondered, "Gosh! Just think of the good a person could do if they had the powers that the statue of liberty must possess!"
Anyway, Lady Liberty then visits Joan in a dream and grants her super powers to aid American troops. Miss America, Joan's new superhero persona, now fights the Nazis with her super power. She turns them into doves! The incredible power to turn Nazis into doves does not exactly come to mind when one thinks of the powers the Statue of Liberty must possess. But at least it was original.
After a few issues, Miss America comics died off. It turns out the power of "Nazi-to-dove-turning" was probably a little dull.
The Joan Dale character was resurrected briefly in 1984, with a cooler super power. This time, she could control molecules- meaning she could do practically anything! But even with this cooler power, Joan Dale quickly died out. And with Joan went the last vestiges of Miss America.