The new Gotham Knights video game gives a deep dive into the minds and worlds of Batman's family members: Nightwing, Red Hood, Batgirl, and Robin. These are far from the only members of the Bat-Family in the comics though, as there are numerous who make it an extended family.
The game also hints at what could be considered close friends of the Bat-Family via in-game emails from characters of the DC universe. In the comics, there are many DC heroes who may not always work with Batman's team or even operate in Gotham City, but they will always be on the side of the Bat-Family when needed.
Huntress
Helena Bertinelli
In many cases where Gotham is on the verge of total destruction, Helena Bertinelli AKA Huntress has joined the Bat-Family in protecting the city. However, she never remains part of the team because of how different she is from Bruce Wayne; she has no qualms about killing.
Helena will gladly slaughter a room full of criminals and stand proud about it which often puts her at odds with Batman. Still, Huntress will rise to the occasion whenever Batman needs her, including in the No Man's Land storyline where she temporarily became Batgirl.
Gotham Girl
Claire Clover
It's fitting that Batman would have a lot to do with a hero named after the city that he protects. Though she has only operated with the Bat-Family briefly, Gotham Girl did form a bond with Batman in that time, to the point that the Caped Crusader gave her Platinum Kryptonite to permanently give her powers akin to that of the Super-Family.
The relationship between Batman and Claire Clover is a sweet one, showing a surrogate father/daughter dynamic that is not seen with Batman that often. Sadly, Gotham Girl has not been seen since given the Kryptonite when she could be a strong recurring member of the Bat-Family.
Zatanna
Zatanna Zatara
Despite the many times that Batman has admitted his intolerance to magic, one of his earliest friends is one of the most famous magic wielders in the DC universe. That would be Zatanna, a childhood friend whom Bruce Wayne met because Zatanna's father and Thomas Wayne were friends.
As luck would have it, both kids grew up to be superheroes and members of the Justice League. Typically, whenever Batman encounters magic or a magical villain, he defaults to his old friend for help. These two feel almost like brother and sister as they always have each other's back, even during the darkest times which makes her perfect Bat-Family material.
Green Arrow
Oliver Queen
A showcase of drastic similarities and differences when it comes to Batman and Green Arrow. Both are playboy billionaires by day and vigilantes by night protecting a crime-ridden city. However, where Batman is a broody dark knight, Green Arrow has more in common with Nightwing in terms of personality.
Every battle features Green Arrow throwing out a snappy comeback against his foes. The similarities and differences have resulted in Batman and Green Arrow having a friendship that's filled with as many laughs as well as endearing moments. Even Frank Miller showcased this friendship lasting to their old age in The Dark Knight Returns.
Black Lightning
Jefferson Pierce
As wise and kind as he is powerful, Jefferson Pierce AKA Black Lightning earned the respect of Batman for how much he fights for the people. Batman even recruited Black Lightning to be in The Outsiders, allowing him to be a leading figure for that team.
For a time, Black Lightning actually was a Bat-Family member as one of Batman's few people he trusted during Infinite Crisis and Superman/Batman: Public Enemies. This is a friendship that is not seen often but stands out when it is.
Katana
Tatsu Yamashiro
These days, Katana is more well-known for her involvement with different incarnations of Task Force X AKA The Suicide Squad. However, her mastery of martial arts and relentless pursuit of justice did earn her a spot on Bruce Wayne's secret team of heroes known as The Outsiders as well as Batman Incorporated.
Katana is known for being a Bird Of Prey, which resulted in a friendship with Barbara Gordon that led to her being friends with the Bat-Family. In the sadly short-lived animated show Beware The Batman, the showrunners actually gave Katana more of a presence in Batman's life. She is depicted as Batman's first sidekick, which is a vastly different take on the canon.
Harley Quinn
Harleen Quinzel
There is no denying that Batman's relationship with Harley Quinn is a bit complicated, especially when she had more loyalty to the Joker as his henchwoman. That changed when Harley began embracing more of an anti-hero role in the DC universe, even protecting Gotham as one of the Gotham City Sirens.
In certain events, Harley Quinn has assisted Batman and the Bat-Family in the protection of the city; romance has even been hinted at between Harley and Batman. One of the best examples of this comes from the Injustice comics where Harley is as much of a respected hero as Batman as well as his partner in the future where Superman is a ruthless dictator.
Catwoman
Selina Kyle
This character constantly shifts between villain and anti-hero which keeps her from remaining at Batman's side, resulting in an often toxic DC relationship. If Catwoman were to settle down and completely reform, Selina Kyle would without a doubt become a stand-out member of the Bat-Family.
In the numerous situations that have forced Batman and Catwoman to work together on cases, they prove to be as much of a Dynamic Duo as Batman and Robin are. Batman: Hush really showcased how much of a good superhero Catwoman can potentially be and could be a valuable part of the team.
Black Canary
Dinah Lance
The history of both Batman and Black Canary is surprisingly intertwined since both heroes were trained under Ted Grant AKA Wildcat. Dinah and Bruce see and despise the criminal element that plagues Gotham and strive for a better tomorrow. As a result, the two martial arts masters tend to work well together, even sharing a connection with Barbara Gordon on their teams.
Dinah is also a close friend of Barbara Gordon AKA Batgirl, a friendship that bloomed into a close friendship as they worked together as members of the Birds Of Prey. So whether it's from Bruce or Barbara, Black Canary and her husband Green Arrow would quickly join the Bat-Family at a moment's notice.
Superman
Clark Kent/Kal-El
At this point, very little needs to be said about this friendship; they are total opposites that found common ground to the point that their families actually end up coming together for the holidays. While fans love to see them fight, there is a reason that they are nicknamed The World's Finest, they are DC's greatest heroes as well as friends.
Bruce and Clark have had each other's backs for years they come across as long-lost brothers. They may disagree with each other on certain things or get into fights, but they would also die for each other. If anybody can be considered part of Batman's family, it's Superman.