Everyone on Avatar: The Last Airbender, especially since the characters of both genders tend to be martial arts experts, possibly with elemental manipulation powers. Hell, The Dragon and her two friends are female, and it would really get in the way if Aang or Zuko refused to fight someone throwing lightning at them.
The sequel series The Legend of Korra likewise does not have anyone hesitating for a second to hit women. Korra, Lin and Asami have all had various male characters trying to seriously hurt them, but being in a World of Badass they can give as good as they get.
Terry, Bruce Wayne's successor, in Batman Beyond. Really, his policy isn't based on gender, but based on whether the person he's fighting is a good person or not. He'll always avoid hitting innocent victims who are just unfortunate enough to happen to be under the control of the Monster of the Week, or something along those lines. However, there was one incident where he avoided hitting two girls who were fighting him...by tricking them into fighting each other. He was grinning the whole way through.
Sterling Archer of Archer clearly loves women but has no qualms about knocking a female enemy out cold, taking out a female target, or just smacking a woman a good one to get a hold of herself. Being an spy, he's probably aware of the risk of being lenient on dangerous women.
Cartman from South Park has no scruples about anything else, so it's no surprise he accepts Wendy's challenge to a fight, and he gets in a few good hits until she bashes his head into the metal climbing equipment, leading to a supremely deserved No-Holds-Barred Beatdown.
Kenny is shown beating a female bully in the episode "The Poor Kid". DO NOT mess with his little sister, Karen.
In "Faith Hilling", Kenny is also shown beating up the two rival girls who were doing new memes.
During the climax of the first part of a 2-part episode, "The Cat and the Claw", Batman finally comes face-to-face with Starter Villain Red Claw, a mysterious international terrorist leader who turns out to be a woman. During their fight, Red Claw asks if he's surprised to learn that she's a woman. Batman knocks her down with a sweep kick and quips "I'm an equal opportunity crimefighter."
At least two counts with Poison Ivy. In her premiere, Batman decks her while tangled up in her plant monster to get at the antidote. In "Almost Got 'im", Batman punches Ivy away to prevent her from trying to take off his mask.
In "Mad Love," The Joker hits Harley Quinn across the face so hard she flies across the room. And then he pushes her out a window.
In "Chemistry," Poison Ivy is about to give Batman the kiss of death, then Robin interrupts and says "kiss this!" before knocking Ivy upside the head with a pipe.
Taboos against hitting women are usually nonexistent on Celebrity Deathmatch. (Of course, they tend to hit back.) However Mills Lane says that usually, he doesn't do so, but he makes an exception when Judge Judy tries to take over his ring. (As Nick and Johnny say, making Mills angry is never wise.)
When Mrs.Manface gets her mech disarmed, she tries the line, but Batman only says: "The Hammer of Justice is Unisex!" and floors her.
In a Freaky Friday episode, Batwoman (a corrupt heiress, not the usual one) has switched bodies with Batman. Amusingly, Batman (in Batwoman's body) tries the "Batman would never hit a defenceless woman" line. Batwoman (in Batman's body) simply responds with "Funny, I don't have that problem" and decks him.
Danny Phantom: Danny has no problems fighting Ember, Desiree, or Spectra and knocking them around in the same way as his male adversaries. However the fighting is nearly all done with "ghost rays" or certain weapons where it's a fair fight rather than fists. Danny does not actually hit them and avoids hurting Valerie when he fights her.
Fairly OddParents has a couple of occasions where a character is fully prepared to do this, but is prevented from doing so:
In "Kung Timmy", Francis threatens to hit Tootie after she intervenes in his fight aainst Timmy. This is enough to push Timmy's Berserk Button and give him a Heroic Second Wind, since he's now fighting to defend Tootie and not just for vengeance.
In a later episode, he and his grandfather are transported into an old black-and-white cartoon, where they encounter a Dastardly Whiplash-esque version of Vicky. At the end of the episode, Timmy's about to knock seven bells out of her when his grandfather objects that you can't hit girls in old cartoons. Timmy immediately wishes that Vicky was a boy, and then knocks seven bells out of him.
Family Guy lampshades this in an early episode where Lois learns martial arts and an all family brawl breaks out. Later, Peter can be seen tossing Lois into the trunk of a car, smashing Connie D'Amico's face into a fire extinguisher, and shoving Meg to the floor for no reason. Peter has also been known to mercilessly beat 8-year-old Lucy (of Peanuts fame) in retribution for pulling the ball away from placekicker Charlie Brown, a parody of the recurring comic strip gag; he gives her one final kick — to knock her unconscious — for not being a licensed therapist.
And in the beginning of the infamous family brawl scene, after Peter hits Lois:
Lois: You can't hit me! I'm a girl!
Peter: Sometimes I wonder.
While most of Peter's physical abuse toward women was (ahem!) played for laughs, it is played straight and dramatically in episodes featuring Quagmire's sister trying to flee her abusive ex-boyfriend. It's all over now.
Joe did punch Lois many times in the episode "Breaking Out is Hard to Do" after he catches and arrests her for stealing. He explains that regulations require him to treat all suspects the same way, regardless of gender. She was very understanding of the whole situation.
"A Fistful of Meg" – The Season 12 episode where a bully, who is more than a foot taller and 200 pounds heavier than Meg, threatens to beat Meg to death in the most brutal way possible. He actually does hit her during their fight, but Meg is able to hold her own.
Arthur plays this straight in "Arthur's Big Hit" when D.W. takes Arthur's model airplane even though Arthur told her repeated not to touch it and throws it out of the window, obviously too obtuse to learn that model airplanes don't fly. When Arthur sees the damage, he gets furious at D.W. and punches her in the arm out of pique.
Hey Arnold!: In the episode "New Bully on the Block," fifth grade bullies Wolfgang and Ludwig beat up Helga Pataki twice.
The Powerpuff Girls: The villains have no problem not only attacking three girls but three kindergarten-aged girls. To be fair though, they are villains, and the series would be pretty boring if nobody was willing to fight the protagonists.
Jonny Quest: The Real Adventures: In one episode Race gets into a fight with Julia, knocks her out, and then says "Pop always said it's not nice to hit a lady. But then again, Miss Julia, you're no lady."
Jonny also has no problems with trying to display his martial arts skills against the Daughters of Zin.
Speaking of Zin's twins, normally peaceful and serene Hadji of all people throws down in a surprisingly brutal fight with one of them, at one point punching her straight in the face.
In X-Men: Evolution, Avalanche or any of the Brotherhood boys has no problem fighting female members of the X-Men. Though not actually hitting, Avalanche does one better and used his power to create earthquakes to attempt to kill Kitty twice before Season 2 rolls in.
The Girls' Night Out Episode "Walk on the Wild Side" has the girls form a vigilante group. When confronted by a chop-shop gang, Amara mockingly reprimands the boss about his mother telling him not to get in fights with girls. He responds it's too bad he never listened.
Implied in Ed, Edd n Eddy's Big Picture Show. Eddy's Brother mistakes Edd for a girl and not long afterwards uses Eddy as a club to pound him into the ground.
Ironically, despite being usually depicted as the nicest of the Eds (and probably the nicest character in the show, besides perhaps Nazz), Double D nearly attacks Sarah in "Is There An Ed In The House?" (Ed holds him back, of course), and he tries to fight the Kankers as 'The Masked Mumbler'. He gets utterly crushed, of course.
Another episode has the Camp Straight Jimmy attacking Nazz after he suspects her of stealing his shampoo. It's presented more like a Cat Fight than anything else but Sarah is visibly shocked.
Played with when Giganta suddenly asks Superman if he would hit a girl. Superman stops in midair, unsure of what to do... and then Wonder Woman takes her down.
In The Smurfs episode "The Smurfette" (a cartoon adaptation from the comics), Hefty attempts to hit Smurfette when she admits she's taking orders from Gargamel. Sort of justified in that Smurfs had no idea what a female was in regards to their own kind at that point.
The dragon from "Dragonshy" beats up Pinkie Pie off-screen and blows Rainbow Dash out of his cave after she kicks him. He very likely would have done further damage had Fluttershy not intervened.
In "Lesson Zero", Mayor Mare takes Twilight's favorite toy, Smarty Pants, away from Big McIntosh who then shoves dozens of mares out of his way in an attempt to reclaim it. Justified as he was under Twilight's spell at the time.
In "Putting Your Hoof Down", Iron Will throws Pinkie Pie and Rarity around and then into the mud when they try to stop him from reaching Fluttershy's cottage, then later threatens that Fluttershy will be in a world of hurt unless she pays up the money she owes him. Fortunately, the situation gets resolved peacefully.
Daring Do gets into a Big Ball of Violence with Caballeron's Mooks in "Daring Don't". And Ahuizotl's worshipers try to attack the Mane 6.
In Twilight's Kingdom Part 2, Tirek has no problem with physically manhandling Celestia as well as Twilight whom he throws into a mountain followed by tackling her THROUGH it. When offering Twilight's friends in exchange for the alicorns' magic, the clearly implied bargain is the magic for their lives.
The trailer for the fifth season of Samurai Jack shows Jack gunning down the Daughters of Aku with a machine gun. (Of course, they're a group of merciless assassins out to kill him.)
Even before the Darker and Edgier fifth season, Jack showed that while he's undoubtedly an honourable warrior and a nice guy, he won't pull his punches on women who pursue the bounty on his head. Just ask Josephine and Princess Mira.
Scooby-Doo, Where Are You!: In "Jeepers, It's The Creeper," Velma is cornered by the Creeper. She asks "You wouldn't hit a person with glasses, would you?" The Creeper removes Velma's glasses from her face and winds up to sock her. The trope is averted as Velma kicks the Creeper in the shin and retrieves her glasses before running off.
In Star vs. the Forces of Evil, none of the villains hesitate to physically attack Star Butterfly. Hero Marco Diaz was willing to tackle Ms Heinous (an evil old woman) to the ground and twist her arms.
The title character of Arthur apparently would, if punching DW in "Arthur's Big Hit" is any indicator.
Soos fries a female AI attacking him and his friends by throwing her disc in a pizza oven.
In the finale, it's implied that Bill was about to kill Mabel by "random choice" (between her or Dipper) if Ford had not gave him the equation to getting rid of the barrier trapping him in the town.
T.U.F.F. Puppy: Accidental or not, Dudley shows that he often has no qualms against hitting Kitty and causing most of her injuries in the first place. One episode shows he has absolutely no qualms against using her as a golf club to attack anyone whom he mistakes as the Chameleon (one of T.U.F.F.'s enemies).