Batgirl is a DC comics character that dates back to 1961. She was first introduced as a sidekick partner for Batwoman. Bat-Girl was Betty Kane, niece of Kate Kane. This character lasted only a few years. She didn't bust a lot of criminal heads, she mostly just swooned over Robin...
In 1967, DC took another crack at Batgirl, this time making her Barbara Gordon, daughter of Police Commissioner Gordon. This version lasted throughout the silver age with very little change to her costume or story line for thirty years...
Later in that same year of 1967, the TV show "Batman" decided to add Barbara Gordon to their show. They kept her story very close to the comics but the costume they made for actress Yvonne Craig was purple and Yvonne developed a cult following for her portrayal as Batgirl. I would know, I was one of them...
While the Batgirl character faded in popularity in DC comics, the Batman movies were doing well in theaters from 1989-1997. The last of that series, "Batman and Robin" by director Joel Schumacher reintroduced Batgirl but Schumacher took a lot of creative license with the film and wrote her as Barbara Wilson, niece of Alfred Pennyworth. The film was a flop and killed the series with an unmade sequel that never got filmed. Actress Alicia Silverstone won the Razzie award for worst actress of 1997 for her role as Batgirl. The film made top 5 worst films of the 20th century. Thank God, Chris Nolan revived the Batman franchise with Christian Bale.
While not much was happening with Batgirl in the comics during the 90's, there was a graphic novel called "the Killing Joke" which told a dark tale of the Joker trying to drive Jim Gordon crazy and turn him into a killer. The Joker shoots Barbara and the bullet damages her spine making her a paraplegic. DC eventually decides to run with the idea to rejuvenate her character. Barbara fights on from a wheel chair, honing her detective skills in the cyber world. She uses the alias "Oracle" and starts up the Birds of Prey, an all female crime fighting unit in Gotham.
The Birds of Prey were a hit, and there was even a short lived TV series where actress Dina Meyer played Barbara Gordon/Oracle. The comic run lasted from 1999 into the 2010s but in 2006, DC decided to bring back Batgirl with a twist. Barbara was still Oracle but they decided to put Helena Bertonelli (who was already Huntress) into the costume. She didn't last a single issue as she broke the code and lost her privilege to wear the bat. By the end of that same issue, Cassandra Cain was wearing it instead. Cassandra was an orphan, daughter of a master assassin who had taught her a few things in her youth. Cassandra was mute and illiterate. Batman and Barbara both train her to be Batgirl. She is dark and terrifying and covers her entire face in the hood. She lasts as Batgirl for 5 years. She is sometimes referred to as Black Bat.
After a time, Cassandra was injured and disillusioned so Barbara sought out another replacement. This time she went to Stephanie Brown. Stephanie was an energetic and eager crime fighter. She started out as Spoiler and was then taken in by Batman and made the fourth Robin. Barbara made Stephanie a suit that reflected her Spoiler costume and she and Cassandra helped train her. Stephanie was the Batgirl for a couple years until DC did their big overhaul in 2011 with their New 52 launch.
The New 52, was a consolidation move for DC. In one move they created a single story line (no more multi-verses) for all. They decided to bring back Barbara as Batgirl. The story goes that Barbara gets her spine repaired in South Africa with some experimental science and as she can walk again. She trains hard and puts the bat suit on again, this time a slick black and gold version. As for Stephanie and Cassandra, they are still around but as Spoiler and Orphan respectively. The black suit for Barbara is not entirely new. The comic web series "Gotham Girls" had Barbara in black and gold and the comic version might have been inspired by the 2002-03 TV show Birds of Prey. Dina Meyer was Oracle but they often showed flashbacks of her as Batgirl, pre wheel chair, wearing this suit. She put it on again for one episode using a risky nerve bypass device in her back so she could fight Lady Shiva. This suit is also the de facto suit for the video game "Arkham" series.
One DC comic run in 2014 was called "Futures End". In that run, Barbara puts together a League of Batgirls. This group includes herself, Cassandra, Stephanie and a new comer, Tiffany Fox. For Batman fans, Lucius Fox is Batman's tech guy. He invents all the cool gagets. In the TV show Batwoman, his son Luke Fox is Batwoman's tech guy. Luke also has a sister named Tiffany. Tiffany has been a Batman fan since she was a young kid. She becomes Barbara's latest recruit and joins the League of Batgirls.
That brings us to the next re branding of Batgirl. Someone decided to modernize the character, kind of threw out most of the history and came up with a character more suited to the modern age. The story goes that Barbara has a fire in her apartment and loses everything. She decides to start over fresh in Burnside, the hip, swank suburb of Gotham. Barbara returns to university and creates a new DIY costume. She is into social media and takes a lot of selfies. It has been a hit and the look was adopted into the newer animated shows, including Harley Quinn.
I round this off at ten even though there have been other variations including the Rebirth line. Her rebirth costume however is not much of a stretch from her new 52 look but with a mask instead of a cowl and some of the old blue in it. Some of the animated shows had slightly different looks too with some combinations of her silver age look involved. I left out Helena too who was Batgirl for maybe 15 pages only. Besides, she will always be the Huntress in our hearts.