Both, the heroes and villains in the Double Dragon series, have no qualms about beating up women. Williams punches Marian before taking off with her during the opening of the original game, while the Lee brothers are required to beat up the whip-wielding Linda enemies (among the various other thugs they face) in order to fulfill their mission.
Bully. If you want, you can punch any random girl in the face, but doing so instantly maxes out your Wanted Meter and causes prefects to spawn out of nowhere to bust you. As such, most players Wouldn't Hit a Girl, if only for practical reasons.
For the record, in Bully you can also punish your girlfriend for cheating on you by shooting her in the face with a spud cannon. And the next time you want a kiss from her, all you need is some flowers. Unless you're a great artist, in which case she'll kiss you for free.
In Fallout 3 you get all kinds of nasty women attacking you, from homicidal cannibalistic raiders, to slavers to mercs who are contracted to kill you. They'll happily attack you with baseball bats, knives, pistols, assault rifles and grenades. Killing them (preferably by exploding their heads) is necessary for your own survival. Sexism is most definitely obsolete in the wasteland.
Final Fantasy IX The closest to someone who wouldn't is Zidane Tribal, the Chivalrous Pervert who has an ability called 'Protect Girls', and in Dissidia: Final Fantasy says when up against Terra 'A girl? This'll be tricky...' but with no effects on gameplay. However, in his own game he has no compunctions about fighting and killing the Alexandrian soldiers when they're invading Cleyra or trying to stop him from rescuing Dagger.
As proven with General Beatrix and Lani, he will fight women without a problem, and in some cases flirt with them too.
The God of War series. Kratos has no problems whatsoever harming women or men alike, because he sees everyone as equally worthless. Yes, he's pretty much a Villain Protagonist.
Very slightly averted at times, specifically when said woman reminds Kratos of his late wife or child for whatever reason. That usually cools him off a bit. Maybe. And temporarily.
The Hitman series. Not only does Agent 47 take innocent women hostage, but it's mandatory to knock out and even kill a number of them throughout the games. 47 actually shows his first ever sign of anger towards a female character, we're pretty sure that if he got ahold of Diana before he passed out, things would have been pretty damn messy.
Agent 47 would pretty much kill anything if it compromised his line of work.
Kingdom Hearts: Sora doesn't pull punches against female opponents, be they actual villains (Maleficent, Ursula, Larxene) or sparring partners (Selphie, Yuffie, Tifa). Likewise, none of Aqua's male opponents go easy on her. Not that they need to.
The Legend of Zelda series. Ganondorf not only kidnaps and imprisons Zelda repeatedly, he is indeed willing to backhand her.
MadWorld Jack apparently has no problem with hitting women. From female boss fights to the mayor's daughter. Although the finishers on the female bosses are quite a bit less violent than those of Male bosses, however that's not saying a lot for this game.
However they cater heavily to the Ryona fetish, his style of finishing them is to spank them or force him out of their sexually suggestive attack to their deaths.
In Anarchy Reigns however, he ends up sparing Rinrin after defeating her. In return, she later comes to help him out in a boss fight against Cthulhu.
Likewise, his predecessor Gene from God Hand had no problems fighting female mooks. Sometimes they just need a little spanking.
Super Mario Bros. series. Paper Mario and Mario & Luigi? There's plenty of main female villains in the series for Mario and Luigi to fight, and your battles against them go the exact same way as against any other enemy or boss.
Wario too, at least his willingness to just as well battle Captain Syrup every third or so boss battle in Wario Land 2.
Shepard — regardless of gender — has a Renegade option to punch a female reporter who has been asking him/her trick questions aimed to either ruin his/her reputation, or to estrange humanity from alien species. As the reporter in question was exceedingly punch-worthy for reasons unrelated to her gender, the punch is often considered a Crowning Moment of Awesome and the option is even repeated in the second game. And the third, though this time she's wised up a bit and dodges. Then Shepard headbutts her.
The series in general follows the trope, as many enemy and friendly combatants are female (and not just the feminine Asari). Nobody, Renegade or Paragon, seems to have any qualms about gunning them down.
The third game also includes a cut scene during one of the optional side missions where Shepard, as he goes to rescue a character who has been kidnapped by a male and a female mercenary duo, delivers a surprisingly vicious punch to the stomach of the female baddie - so much so it's strongly implied she may be dead.
Max Payne. At one part in the first game he meets Rico Muerte (a hitman) and Candy Dawn (a hooker) in the tenement building bar. A fight starts, and both Rico and Candy pull a gun. In the ensuing firefight, Max takes them both out. And let's not forget about how he deals with the Big Bad, Nicole Horne.
The Meat Boy series Dr Fetus who loves to do that on regular basis.
The Metal Gear Solid series has plenty of female bosses. In MGS4, four of the six human bosses are female, as are the FROG troops. It's wonderfully subverted in MGS2 with Fortune - Snake and Raiden would like to hit her but can't because of her forcefield.
Not to mention the first boss of Metal Gear Solid 2 is Olga Gurlukovich, who both the player and Snake know is pregnant. Snake tranqs her, but solely because he doesn't have a more lethal weapon handy.
MGS3 has the several times Big Boss/Naked Snake fights the Boss, his former mentor. The first few times they tangle, he fails to land a single punch — not because he's deliberately holding back, but because (as he acknowledges) she is simply much, much better than he is; typically she just casually breaks his arm without looking like she's even trying. And his reluctance to face her in the end has nothing to do with her gender and everything to do with his love and respect for her. She's portrayed throughout the game as about as Bad Ass as it gets, never as someone who needs your chivalry.
A Dance with Rogues includes characters who are perfectly fine with or creepily enthusiastic about abusing women, but the most prominent is Vico.
This is discussed via Travis Touchdown, the protagonist of No More Heroes. Although he is hesitant to kill women, he sees no problem hitting them. He battles five female assassins and kills three of them. However, he didn't kill the first he fought; the second was the one who chastised him for not killing her, calling it weakness, not mercy, before killing herself. There were some form of circumstances with the other three as well the first killed his master in front of him, the second bled out after making him admit defeat, and for the last, "It's Personal".
He goes on to fight even more women in the sequel, killing a total of 27 and knocking one out because she was just a teenager. (Also of note is that 24 of them transformed into a Humongous Mecha being piloted by a man, and were the only female mooks in the series. After the fight he comments "I gotta admit though, this leaves a bad aftertaste. I mean, ripping through a bunch of mostly harmless cheerleaders?", though at the prospect of his victory being nullified, he says "Whoah, wait! I mean, they weren't that harmless. You can tear some shit up with a pompom.")
Pokémon Gold and Silver/Crystal and HeartGold/SoulSilver has Rival Silver, a mean kid abusing his Pokémon and most of the time pushing the player out of the way and even seemingly even kicking one in the butt. You can play this as either boy or girl in Crystal, HeartGold and SoulSilver.
For that matter, everytime a female Pokemon goes into a battle against a male Pokemon.
Postal gives the player the ability to kill anybody.
Played with in Sonic Adventure 2. Knuckles has no problem attacking a woman if she threatens the Chaos Emeralds. Following Knuckles' battle with Rouge, she shames him for attacking a lady. However, she slips and almost falls into a vat of lava, from which he rescues her and apologises - reluctantly - for hurting her.
Of course Rouge had been attacking him just as much, so it might qualify for a case of self-defense. Not to mention he apologized to Rouge, after she gave Knuckles back his Master Emerald pieces to thank him for saving her, even if she doesn't openly admit it.
Splinter Cell Conviction: In the story, Sam Fisher punches Anna when he finds out that she faked the death of his daughter to make him less distracted. He then hits her again. The first was because she deserved it. The second was to make sure she was hurting.
Tales of Monkey Island: Near the end of Chapter 5, LeChuck strikes Elaine for trying to protect her undead husband Guybrush. Note that Elaine is the woman whose hand in marriage LeChuck's sought for over a decade. It's mysterious how he expected her to accept him after that, but then again it's pretty mysterious how he ever expected her to fall for an evil undead criminal with a long history of attempting to kidnap her and force her into marriage.
Tekken 5: In a cutscene during Story Mode, as Feng Wei prepares to fight Asuka Kazama, she protests that not applying Wouldn't Hit a Girl would be a disrespect. He answers that, as fighters, if he held back, that would be disrespect.
Thrill Kill: Mammoth not only has to beat both genders of people to death in the game to get out of hell, but, in a fit of beastly aggression once back on Earth, grabs a little old lady from the street and relentlessly shoves and pounds away at her body until she is completely inside a postbox.
Mega Man presumably has no compunctions against this, as he fought Splash Woman in Mega Man 9 without any more concern than for the other 7. Every boss does this if you play as Roll in Mega Man Powered Up (Though Cut Man's reason for attacking her is that he's outright terrified of what Roll will do to him if he doesn't defend himself).
Zero is also an equal-opportunity killer in his own series, though the one girl he fights during the Mega Man X series happens to have been his girlfriend and thus causes serious BSOD when he is forced to kill her.
Return To Krondor plays this trope straight. Bear not only hit Talia, but he murdered her and worse. There are only a few enemies that are female, but your male characters can kill them without any comment (the one female character you play makes no comment about that, either). Those few female enemies would cheerfully kill you anyway. The mostly male enemies are completely willing to kill anyone, regardless of gender. In fact, Big Bad Bear says "You will give me the Tear, or we will slaughter you to the last man! And...wooman!" That does not even cover the goblins, vampires, ghouls and other creatures.
Hell a lot of the Kombatants are women so it helps your case when the women are just as willing to kill you as the men. Maybe.
In Prototype, there is exactly one female optional target in the Web of Intrigue, and Alex will attack, kill, and eat her the way he will every male target: viciously. Depending on the player, he'll extend the courtesy to female civilians. Elizabeth Greene is not excluded from being beaten to death and devoured, though refraining from hitting her probably doesn't count as chivalry. Alex likely doesn't care either way because he's a bastardand because gender-specific human rules like chivalry are stupid when you're not human, lack inborn sexual characteristics, and can switch gender like switching hats.
The Blackwatch creed does not make exceptions for comrades, countrymen, or non-combatants; it definitely makes none based on sex. If they may be contaminated, women get gunned down just like men.
Parodied in the NES game Day Dreamin' Davey, when Davey has to destroy the Cyclops in the "Ancient Greece" dreamland by striking him in the eye. It turns out that the "Cyclops" in his imagination is a girl in class... whom he just hit in the eye! Oh Crap!
Starfy from the Starfy series has no problem with hitting and defeating female enemies like Numan and Puchi Ogura #5 (From Densetsu No Stafy 2), Dejeel (Big Bad of Densetsu No Stafy 4), and Snips (From The Legendary Starfy).
Cole in Infamous hits Sasha in the first game. In the sequel, it's Kuo or Nix in the end, depending on which alignment he is on.
Through at least its 2011 release, most of the WWE's video game releases allowed men to fight against women, with — save for match types specifically for women — no restrictions were placed on the match type or stipulations. This means a player could (for example) set the game to have The Great Khali battle Kelly Kelly in a no-disqualification, first blood match; Beth Phoenix take on The Big Show in Hell in a Cell (a modified steel cage match); or Kane vs. AJ and Kaitlyn in a handicap Ambulance match (a match similar to the stretcher match, where the objective is to injure your opponent to the point where they are taken from the arena in an ambulance). It is unclear exactly why the more recent WWE video games have disabled the option of "man vs. woman" matches.
With the inclusion of female created players in NHL '12, this is now possible in the NHL Hockey series.
In The Godfather games, while there are no onscreen female mobsters, several store owners are female and it is perfectly possible to visit the same "negotiation" techniques on them as on their male counterparts.
Alpha Protocol: although most of the enemies in the game are male or, if female, are soldiers/fighters, there is an option during an early mission where the player can choose to perform a stealth knockout (with punching) or even a stealth kill on a pair of innocent female bystanders (dancers on a yacht).
Any fighting game with a mixed-gender roster is going to have this, whether it's invoked or not.
In The Elder Scrolls V: Skyrim, the player character will frequently fight and kill female opponents. This is not considered unusual or socially unacceptable in the setting. The player can also sometimes perform "finishing moves" on enemies that result in fairly gory kill sequences, and these can be performed on female enemies the same as male enemies.
If you complete a quest for the priestesses of Dibella (goddess of women, among other things), you are blessed with a permanent damage bonus against the opposite sex. Meaning, if you play as a male character, the goddess of women has specifically blessed you with the ability to murder women more efficiently.
In the The Witcher 2: Assassins of Kings you have a chance to take place in a tournament, generally beating up the strongest soldiers in the army camp you're currently staying in. After defeating a couple of opponents one of your female allies will ask to fight you. She'll comment on how she's glad you didn't go easy on her and then sexy times await.
When Yuri and Judith are captured and imprisoned in Ghasforast in Tales of Vesperia, they decide to distract the guards by beating each other up. They actually seem to be having a whale of a time. Seeing as they're both Blood Knights, this isn't surprising. Meanwhile when the party fight Schwann at Baction, he shows a certain reluctance to fight a 'lovely lady' like Judith, but this is probably more a hint that Raven's still in there somewhere, because he shows no reluctance about hitting Rita (though to be fair, she's always hitting people undeservedly) and Karol, a male child. The main villain also has no problem with capturing, torturing and brainwashing a female character.
In the World of Warcraft novel, Tides Of War, Garrosh backhands Kelantir Bloodblade, a female Blood Elf paladin. This is portrayed as a Kick the Dog moment, not because Kelantir is defenseless, but because all she did was meet with like-minded individuals to discuss her concerns over Garrosh's actions.
The Combatribes had Martha Splatterhead, the Big Bad of the game and cyborged-up final boss. She asked Berserker, "You wouldn't hit a lady, would you?" Cue her getting trashed by Berserker, who says "CYBORGS AIN'T LADIES!"
The first of the Kunio Kun games, Nekketsu Kōha Kunio-kun (Japan) aka Renegade (US), had members of an all-girl gang the player had to fight against. Given the pre-boss females had either a mace (US) or a handbag (Japan) for the weak-attack ladies and chain whips for the strong-attack ones, and the boss female is a BIG fighter who's only open to a running back kick.
In Ace Attorney, Godot would absolutely hit a girl. Or stab, whatever.
Also in the second game, Phoenix can slap Lotta.
Half-Life can turn into this with the arrival of Black Ops. Their speed, damage, accuracy, and the general difficulty of their fights makes them serve as a Berserk Button for some players, prompting them to use the most brutal methods, like gibbing with the grenade launcher or crowbarring.
Both the Shai-Gen and the Volk in Crackdown have female Mooks, as well as female Generals, and the Agent wastes them as easily as the men.
BlazBlue. Granted, it's a fighting game, so of course this would normally qualify the game as an unremarkable example, except for one thing: when the vast majority of the male characters do it, it seems to be mostly born of pragmatism, and in fact Ragna and Tager both openly say that they have moral compunctions about hitting women. The sole exception is Hazama, who actually seems to enjoy hurting women in particular, physically if not psychologically as well. Of course, this is intended to make us hate him all the more.
In Perfect Dark you are playing as a woman, and your enemies are perfectly willing to shoot or punch you. This is only fair, given you're trying to kill them as well. It would also be a pretty boring game if they didn't.
Batman in Batman: Arkham City is entirely willing to hit his female opponents, who to be fair are trying to kill him. Notably however, his finishing moves on them do not include breaking bones, unlike his male opponents.
Each game in the Sly Cooper series has a female villain who is required to be fought to advance the story. In fact, the Big Bad for the second game is Neyla, who is fought twice in the game; by the end, she has even become an immortal beast who runs on hatred.