James Whitbrook gave us an in-depth look at the decades-long history of Batgirl, and rightly identified the abuse the character's suffered. But: in reading his article, I found myself smiling in spite of myself, because there is absolutely nothing you can do to keep Barbara Gordon down.
There's no one recipe for comic book greatness: Two of the best chances a character can have: they need to be timeless... or they need to be able to change with the times. Barbara Gordon manages to pull off a bit of both.
What Makes Barbara Gordon Timeless
Ever since her introduction, the daughter of James Gordon has been a force to be reckoned with. In almost (if not) every incarnation, becoming Batgirl was her idea— she didn't ask Bats' permission to don the cape and cowl, she simply took it up because it needed doing. (Batgirl: Year One is a great rendition of this, and meshes neatly with the latest incarnation of Babs' Batgirl persona.)
Then The Killing Joke happened. And Barbara never gave up.
Everyone knows about Oracle, Barbara's 2nd crime-fighting career. Her desire to do what's right has never faltered. She's never been afraid of hard work.
If there's the slightest doubt in your mind, I will point you to that time Barbara got a Master's in Law from Harvard, via correspondence courses. She's a bad ass in so many categories, it defies quantification.
While her methods have changed as necessity demanded, Barbara's heroic will has proven unbreakable. She fills one of the most important requirements for a quality superhero: she is a role model.
What Barbara Gordon Has In Common with The Doctor
Certain heroes like Batman and Spider-Man are bound by what defines them. There have been small hiccups along the way, but by and large, Bruce Wayne in the comics has been a consistently dour, unhappy, batarang-brandishing stick in the mud for decades.
Likewise, Peter Parker's almost always been an optimistic, hard-working underdog whose personal and professional lives have been a disaster.
Then there's the Doctor. The protagonist from Doctor Who, he's gone through over a dozen incarnations with vibrantly different personalities and attitudes. He and his beloved TARDIS have gotten overhauls every few years, in an effort to keep the show fresh. It's never the same thing for too long; variations on a theme.
Now look at Babs. She's gone through any number of changes, over the years, personality wise. She started off as pretty care free, a crime fighter who enjoyed crime fighting. That's not exactly unique, but cracking a smile when you're wearing a cowl is harder than it sounds.
Babs has been vastly more flexible in execution than her counterparts. Batman has been dead serious since the late seventies, and has rarely cracked a smile since. Peter Parker's almost always been a goofball. Barbara's been able to change and meet the challenges of the day, whether as a free-spirited crime fighter, a recovering survivor of trauma, a young woman pushing through painstaking physical therapy, and back 'round full circle to the happier counterpart to the Dark Knight.
Through all this, she's always been depicted as smart, dedicated, and passionate. Her journey in-universe has been a gripping one. As a character subject to reinvention in our world, she's been captivating to watch. It's part of the reason she's consistently been viewed as one of DC's most popular characters, period.
And yes, per Mr. Whitbrook, she's been through a LOT of awful mistreatment, both from characters and the creative teams behind her adventures. But for all her trials, nothing has ever broken her indomitable spirit.
Barbara Gordon is, in a word, amazing.