The Birds of Prey were a team that was defined by its core three members, Huntress, Black Canary, and Oracle. It was also anchored by the great writing talent of Gail Simone, who is still the series-defining writer. What was great about the series is that it helped take more unknown characters and allowed them to push up to the forefront, showing off what great characters they could be.
It worked wonders for many of the characters and unlike the movie, didn't need a popular character like Harley Quinn to help hold it all together. All of these characters ended up in Simone's seminal run, in one form or another.
10 Big Barda
It's strange thinking of a New God on a street-level team like Birds of Prey, but that's exactly what happened when the team got a hard reset towards the end of Gail Simone's iconic run. She was introduced after a prison break during issues 99-100 to help bring in new life to the team after fighting expert Black Canary left. She wasn't a long-standing member, meeting her end during the Death of the New Gods, but was at least honored as a member in a later issue.
9 Misfit
When she was first introduced, Misfit was only an annoyance to Barbara, a young and inexperienced girl who was trying to run around being Batgirl. In a city like Gotham, that's dangerous, even if you have metahuman powers as Misfit did. Barbara tried to dissuade her at first, showing her autopsy photos of Stephanie Brown, but eventually warmed up to the girl after finding out she'd been living on the streets and welcomed the girl aboard.
8 Manhunter
Martian Manhunter isn't the only Manhunter running around DC comics, Kate Spencer existed as well. She was a prosecutor who grew fed up with seeing criminals escape punishment, taking up the mantle of Manhunter—a vigilante that was far more extreme than any of the other birds.
She was far more like Frank Castle, providing a nice moral wrinkle to the team that Huntress no longer presented. Just like with Frank, that wrinkle eventually led to her leaving the team.
7 Judomaster
Recruited along with Manhunter and Big Barda, Sonia Sato was there to help break into a Mexican prison. Her stint was far shorter than the others, never getting developed nearly as much as Manhunter did. She was more a background character than anything else, there for her abilities and nothing more. Thankfully, she did manage some further development when she was picked up by Justice League America at least.
6 Lady Shiva
Lady Shiva and Black Canary haven't always been on the best of terms, often coming to blows for various reasons in books. Considering her job, it isn't all that surprising. What is shocking is that she willingly took Black Canary's spot on the team as Jade Canary so that she could go off to train. While technically a villain, Shiva has always been one with a great degree of honor, making her transition to being part of the team less painful than it would have been with most villains.
5 Gypsy
Her role with the Birds of Prey was a minor one, never really making a huge impact on the team. She's a metahuman who utilizes illusions, allowing her to go effectively invisible when she blends into the background.
That power mixed with the interesting way she dressed should have led to a longer stint, but she spent most of her time working with Vixen before departing from the team. Sadly, she'd soon fade off into obscurity as well once New 52 came around.
4 Lady Blackhawk
The least known of the core four characters in Birds of Prey, Lady Blackhawk was essentially the pilot of the team. Her look was wholly unique, having a 1940s flair to it due to the events of Zero Hour displacing her through time and bringing her to the present day. It's an interesting story point, and one Gail explored well throughout the run. While her role was never huge, she was the one who suggested the team be called the Birds of Prey.
3 Huntress
When Gail Simone took over the team, she made it a point to add Huntress, a character that helped round out the team, giving it a much-needed third member. Her penchant for violence as a vigilante helped give a new foil for the team, one that led to some very interesting stories. Without her addition, the Simone run may not have been as career-defining as it was. It's a wonder why she rarely ever appears in animated films or series considering her success in the comic series.
2 Black Canary
When you think of the Birds of Prey, Black Canary is the first person you think of. She's the poster child of the team and one of its original members, right along with Barbara. She was the muscle to Barbara's brains, letting the two friends work seamlessly as a team. Her supersonic scream was also a power you didn't see often, making her fights feel new and interesting. Despite her ties to Green Arrow and the popularity of the show, Dinah will always be a Bird of Prey.
1 Barbara Gordon
After the events of The Killing Joke, it could have been very easy to toss Barbara Gordon aside, making her nothing more than a background character in Batman comics. Thankfully that didn't happen as her pairing with Dinah allowed her to continue to stay at the forefront of DC comics and led to the creation of Oracle, the first paraplegic superhero. It's a shame that she was then made to become Batgirl in later reboots as Oracle was such a unique and great fit for Barbara.