Originally, Superman couldn't fly--he could only run fast and jump very high.

"As originally conceived and presented in his early stories, Superman's powers were relatively limited, consisting of superhuman strength that allowed him to lift a car over his head, run at amazing speeds and leap one-eighth of a mile, as well as an incredibly dense body structure that could be pierced by nothing less than an exploding artillery shell.[101] Siegel and Shuster compared his strength and leaping abilities to an ant and a grasshopper.[102] When making the cartoons, the Fleischer Brothers found it difficult to keep animating him leaping and requested to DC to change his ability to flying; this was an especially convenient concept for short films, which would have otherwise had to waste precious running time moving earthbound Clark Kent from place to place.[103] Writers gradually increased his powers to larger extents during the Silver Age, in which Superman could fly to other worlds and galaxies and even across universes with relative ease.[101] He would often fly across the solar system to stop meteors from hitting the Earth, or sometimes just to clear his head. Writers found it increasingly difficult to write Superman stories in which the character was believably challenged,[104] so DC made a series of attempts to rein the character in. The most significant attempt, John Byrne's 1986 rewrite, established several hard limits on his abilities: he barely survives a nuclear blast, and his space flights are limited by how long he can hold his breath.[105] Superman's power levels have again increased since then, with Superman currently possessing enough strength to hurl mountains, withstand nuclear blasts with ease, fly into the sun unharmed, and survive in the vacuum of outer space without oxygen."

[link to en.wikipedia.org]