In February 1944, DC filed this "ashcan" with the government in an attempt to claim a trademark for the character Supergirl.  Whether such actions had any legal validity is hard to say, but DC filed a bunch of these "ashcans" as did many other publishers. It wasn't until November 1949 though, that DC actually introduced a character who was actually called Supergirl.  William Woolfok and John Sikela introduced a European olympic star and royal princess, Lucy Regent, and dropped her into Smallville for a whirlwind romance.  Nothing much came of it, but the story was reprinted in the Superman in the 1940's trade.
Superboy #5 by William Woolfolk, John Sikela
In August 1951, Lana Lang got her first shot at the Super-Girl name when she's convinced that an ancient helmet gives her super powers.  Superboy indulges her for awhile. Adventure 167 "Lana Lang, Super-Girl" by Ed  Hamilton, Curt Swan, and John Fischetti The Lead mask covers Lana's face but this time she really has super-powers, courtesy of Jerry Coleman and John Sikela. Adventure 189, June 1953
Superboy 36 "Lana Lang, Superboy's Sister" October 1954
In this tale, Lana' parents are lost, presumed dead in Aftrica, so Ma and Pa Kent adopt her.  Clark accidentally sits on her perfume bottle.
And the crooks decide he must be "a dame". 

Previous to that they'd used a geiger counter to track a supposedly radioactive Superboy back to the Kent house, and therefore concluded that Lana was Superboy.  Clark can't disabuse them of this notion without reinstating himself as the likely suspect.  Lana, meanwhile, decides to go along with the gag in hopes of proving Clark is Superboy.

Eventually Lana's parents are found, Clark finds out they sent Lana a radioactive artifact which is the real source of the criminal geiger counter readings.  Superboy shows up and puts the crooks in jail and everything is back to "normal".

Lana, as usuall, has no scruples whatsoever, willing to do anything and endanger anybody to prove that Clark is Superboy. No wonder he chose Lois.

Art by John Sikela.  Written by  Jerry Coleman (probably). 

In June 1957 Alvin Schwartz and Curt Swan (ignore the Wayne Boring by-line) introduced a new character into the daily strip, Myrtle Pepper, given super powers by a blood transfusion from the Man of Steel.  The sequence ran from June to October.  And I really wish I'd ever seen more than this one episode.  (swiped from the Speeding Bullet)
In August 1958 Superman met a real Super-Girl courtesy of a voodoo totem and Jimmy Olsen's imagination in Superman 123.  By Otto Binder, Dick Sprang and Stan Kaye. Jerry Coleman and Creig Flessel gave Lana super powers again in Superboy 72, April 1959. Curt Swan cover.  Maybe Stan Kaye on inks.  (Looks like John Forte to me)
Sales on that story must have been spectacular enough that the decision was made to boot Tommy Tomorrow out of the back of Action Comics and replace him with Superman's teen age cousin, Kara Zor-El in Action Comics 252 May 1959, by Otto Binder and Al Plastino. One of the most infamous  Superboy stories, magic turns the Boy of Steel himself into a girl, in "Claire Kent, Super Sister" by Otto Binder and John Sikela, Superboy 78 January 1960.
"Not a Hoax, not a dream, not an imaginary story!"  The first issue of Lois Lane I ever bought.   And I didn't even feel ripped off afterwards.  Sylvia DeWitt  as Super Woman from Lois Lane 15, February 1960 by Otto Binder and Kurt Schaffenberger. Jerry Siegel, Curt Swan and Stan Kaye gave Lana super powers again (this time as an adult)  in Lois Lane 17 May 1960 and again in Lois Lane 21 November 1960.  The iconic uniform would return again in Alan Moore's "Whatever Happened to the Man of Tomorrow", the last Superman story ever published, back in 1986.
Otto Binder and Jim Mooney couldn't rest until Supergirl had actually met Mary Marvel, um.... excuse me, Marvel Maid in Action 272-3 February 1961. Yet another scheme to prove that Supergirl was ready to be revealed to the world went awry.  Here's Lana again  in Adventure 285 as "Gravity Girl of Smallville" by Robert Bernstein, Curt Swan, and Stan Kaye. June 1961.  The astute will notice this is the exact same story as Sky Girl from 1953.
Jerry Siegel created one of the most insidious villains of the Silver Age- Lesla- Lar, the Kandorian scientist who almost succeeded in stealing Supergirl's entire existence. Action 279 July 61.  One of those multi-part serials DC supposedly never did.  Oddly Linda and Lesla never actually met.  Art by Jim Mooney. Lesla Lar died at the end of her first adventure, but her legacy lived on, as another Kandorian renegade used her equipment to become the Black Flame. Action 304, September 1963 by Leo Dorfman and Jim Mooney.
This one is so convoluted it requires two pictures.  One of those great- "no scene remotely resembling this occurs in this book" covers but Curt Swan and George Klein, shows a super-powered Lana Lang living with the Kents. Adventure 297 June 1962. Well, ok, Lana does have a one panel day dream that resembles the cover, but in one of her wackier schemes to proved Clark is Superboy, she dresses as Superboy herself, thinking that Clark will have to reveal his identity to save her from her own stupidity. Bill Finger and George Papp are the culprits responsible. This story bears a strong resemblance to Superboy 36, above.
And here in Action 289, from June 1962, is a grown-up, non-incestuous version of the character, Luma Lunaii, just perfect for a little cosmic snuggling with the Man of Steel, if only.....
Jerry Siegel and Jim Mooney pull the rug out from under the amorous Man of Steel at the last minute.
Joan Kent, the Super Daughter of Superman and Lana Lang, falls in love with Larry Luthor, the villainous son of Lois Lane and Lex Luthor, in this highly convoluted imaginary story by Jerry Siegel and Kurt Schaffenberger from Lois Lane 46 January 1964.  Larry and Joan were the names of Jerry's own children.
Superboy 105 Siegel And Papp  Prof Langis convinced that a statue of the jungle god Umglikk has given baby Lana super powers.  But it's just Clark, the little scamp.  June 1963
Of course, once Mary Marvel joined the Superman Family, it couldn't be long before Freckles Marvel followed her, could it?  Candy's powers were only temporary in Action 308, but they said the same thing about Streaky. Jan 1964. In the "No good deed goes unpunished" sweepstakes, Debbie Porter certainly takes a prize. After Supergirl generously donates blood to her, she uses her temporary super-powers to try to destroy the Maid of Might's life.
Action 321 Feb 1965. Mooney.
Going way off the reservation, Julius Schwartz, Gardner Fox and Mike Sekowsky created a Super Woman for the Crime Syndicate of America in Justice League of America 29,  August 1964.  In a standard example of What Was Wrong with DC? in the sixties, these characters did not appear again for 15 years. The Phantom Zone is an almost completely male bastion.  Faora Hu-ul from Action 471, created by Cary Bates and Curt Swan in May 1977 was almost certainly a reaction to the inclusion of a female Kryptonian (Ursa) in the Superman movie currently in production.
Laura Kent, the imaginary daughter of Clark and Lois, appeared in Superman Family 200, courtesy of Gerry Conway and Bob Oksner.  March/April 1980 Louise-L, the Supergirl from 500,000 years in the future once switched places with Linda Danvers in order to track down two villains who were hiding in time.  Courtesy of Marty Pasko and Win Mortimer in Superman Family 215 and 16 February 1982 in a story titled "Crisis At the Crossroads in Time!".  The future Supergirl came from a world with an orange sun, with predictable power scrambling results.
Nelson Bridwell and Kurt Schaffenberger introduced yet another Earth-2 doppleganger in the Mr. And Mrs. Superman story in Superman Family 220 (July 1982).  Liandly of Rolez, called "Linda Lee" by Lois Kent, had strange powers including telepathy and the ability to restore Superman's powers when Col. Future stole them.  The series only ran two more issues so she never appeared again. I'm sure there are other Supergirls I'm blanking on at the moment but for now we'll just jump to....

Elliot Maggin and Keith Pollard sock in another trademark when DC finally introduces a real Superwoman in DC Comics Presents  Annual #2, in 1983.