When writer Otto Binder penned the very first Supergirl story, "The Supergirl from Krypton," in May 1959's Action Comics #252, he was already well-versed in the formula of creating female counterparts to popular superheroes. He'd already had a hand in the debut of Mary Marvel in 1942.
Several versions of Supergirl have cropped up over time, but more often than not, her origin remains the same: she is Kara Zor-El, cousin to Superman, sent to earth just before the destruction of Krypton. In the 1980s, she briefly departed from that formula in Superman volume 2 #16, where Supergirl was a protoplasmic creation of Lex Luthor's in a parallel Earth.
All in all, sometimes it seems that Supergirl hasn't really gotten a fair shake as a superheroine. In the '50s, Jimmy Olsen wished her into existence, then decided to wish her out of existence after it appeared that she was "getting in Superman's way."
That storyline seemed to be a meta-statement on the problems of the character, as Supergirl seemed to crop up sporadically each decade, adopted by Fred and Edna Danvers and taking the name Linda Danvers in the '60s, attending college in the early '70s, receiving her own title in 1972 (and seeing it end just ten issues later), and having more attention paid to the changing of her costume design than to her heroic feats.
In 1984, camp reached its height for Supergirl when Helen Slater played her in the critically panned Supergirl feature film. In it, the trend of prioritizing Linda's girlishness over her superheroics (giving her a love interest she's preoccupied with rescuing and pitting her against another woman as the chief villain) continued.
In 1985, the continuity-altering series Crisis on Infinite Earths promised “Worlds will live. Worlds will die. And things will never be the same.” This was nowhere more evident than in the life of Supergirl. Late in the series, a group of DC's most powerful heroes, including Supergirl and her more famous cousin, go off on a dangerous mission to save the universe. On this mission, Supergirl died a heroic death saving the universe and artist George Perez created what is arguably the most memorable cover of the series, with Superman and the heroes of the DCU mourning her loss.
Fortunately, after the '80s, Supergirl's purpose was re-examined. During the mid-90s, Supergirl appeared in the animated series, Superman Adventures, and in the accompanying print run of Superman Adventures presents Supergirl Adventures.
In 1996, Peter David resurrected Supergirl, as a protoplasmic "Earth Angel of Fire" fused with a human girl named Linda Danvers. Supergirl faced off against the vampiric Carnivore and eventually succumbed, leaving Linda Danvers to act on her behalf. In 2002, she briefly appeared again in Supergirl #75.
Finally, though, in Superman/Batman #8, a new interpretation of the original was reintroduced and Kara Zor-El had returned. Not only does she have her own comic book title again, but she also has played a major role in the "New Krypton" story running through the Superman family of titles.