Heroes are, at least for the most part, good people, with clear morals. However, they also have to dish out some punishment now and again, usually directed at people who are decidedly less good, and whose morals are rather lacking, so it's all good.
However, some heroes may feel bad about inflicting any kind of injury on another person, no matter how deserving that person might be. Under these circumstances, the least the hero can do is to let the villain know that, while they may be punching him in the face, they are at least sorry. Very sincerely sorry indeed.
This is even more likely to occur when the character the hero is attacking is not really evil, but needs to be incapacitated for some reason. The hero will say something like "I'm really, really sorry about this," before whacking them over the head or knocking them out in some other way.
However, some people will apologize for attacking even the most deranged Psycho for Hire, even if the psycho's actions left that person with no choice but to attack. Perhaps they're simply someone who Apologizes a Lot.
Alternately, the attacker might not be a good guy, but is still not exactly evil, and does not want to hurt whoever they're attacking. They might be controlled somehow but are still able to speak, they might have transformed into something with a Horror Hunger that they can't redirect, or they might just be unhappy about attacking someone.
Compare Sorry I Fell on Your Fist, where the victim apologizes; Why Did You Make Me Hit You?, where the manipulative attacker merely pretends to feel guilty; and My Fist Forgives You, where the attacker is quickly settling a score. If the attacker apologizes beforehand without explaining why, it's a Preemptive Apology.
Legato's arc in Trigun only ends when he forces Vash to shoot him, execution style, in the head. Vash is really, really broken up about it afterwards.
Quatre Raberba Winner of Gundam Wing. He always asks his enemies to surrender before he has to kill them, then he apologizes for having to kill them. In fact, most Gundam pacifist pilots such as Kira, Uso and Loran say this and ask their enemies to get out of the mechs.
In Ranma ½, forced to stop a rampaging Ryouga, Akane rips off a mooring post from the docks and bashes him over the head with it, yelling, "I'm sorry!" When this fails to even faze him (indeed, the post bent in the shape of his head) she bashes him some more, punctuating each strike with "I'm sorry!"
And in the original manga, Maria Ross apologized in advance before and after slapping Ed across the face for going into Laboratory 5 on his own. Justified since Ed's higher in rank than Maria and could give her and Denny Brosh their walking orders if he wanted to (of course, he doesn't).
Hohenheim apologises before he stabs Izumi Curtis with his hand, although given his relationship with it, it's possible that he was apologising to his philospher's stone.
The First and Second Hokage apologise to the Third Hokage for putting him through trouble, who in turn apologises to the former two for fighting them. It's a long story how they got into that situation.
Though it doesn't strictly count as an apology, the fifth Mizukage expresses regret before attacking Sasuke.
Pain apologises to Jiraiya before making the killing blow.
The undead Second Mizukage and Third Raikage are very apologetic about fighting against the Joint-Shinobi force and even give warnings about what attacks they are about to use. Same goes for former villains Itachi and Nagato, who shout advice to Killer Bee and Naruto while being forced to attack them.
"Colonel Sanders" in the Tournament Arc of Mahou Sensei Negima! apologizes for using overpowered tactics and cheap tricks (that would be downright cheating if there were any rules) in battle. He's sorry for beating you up, but he just has to reach the final match.
In Busou Renkin, when Kazuki is about to kill Chouno, he says that he's sorry. Chouno promptly sticks his tongue out and says, "Don't apologize, you hypocrite." Kazuki then kills him, proving that you don't need to apologize if the person you're attacking is going to be a dick about it afterwards.
In YuYu Hakusho, Toguro invokes this after ripping a monster in half on the order of his client Tarukane: "Not even the best of contracts justifies killing as cruelly as I have just done. I apologize to this creature."
A rather odd example from Neon Genesis Evangelion: during Shinji's battle with the possessed Unit 02, he apologizes before stabbing it - to Asuka, who he's well aware isn't even inside it at the time.
Pilots do tend to get emotionally attached to their machines, particularly someone like Asuka, where piloting it is pretty much all she has to live for. He knew she'd be upset if he damaged Unit 02, so he apologized.
Toji does this when he beats Shinji up out of anger over his little sister getting injured during Unit-01's first fight.
In Monster, Tenma profusely apologizes as he puts the gun to the head of one of Wulf's men.
In ROD the TV, Yomiko apologizes as she rifles the pockets of a mook that she and Anita knocked out.
Syaoran does this to Yukito in the Cardcaptor Sakura manga, apologizing right before punching him in the gut to knock him out so Sakura can use her magic to capture the Firey card.
In AKIRA, Takashi hates using his Psychic Powers, but against someone who just won't give him the chance to explain himself and keeps attacking him ( Mozu, a local Extraordinarily Empowered Girl), he decides to do so... and after the apology, he unleashes a fatal psychic attack. Not to mention he again apologizes to the person he just killed.
Takashi: "I apologize, but you don't leave me any other option... (kills young Mozu) I'm so sorry."
In Bleach, Primera Espada Coyote Starrk apologies to Kyōraku while shooting him in the back with a Cero while the latter tries to attack Wonderweiss, stating the arrival of Wonderweiss means Aizen has lost patience.
In Hekikai No Ai ON, Yuzuki apologized at Seine while throwing her to the deep zone of a pool knowing she can't swim, but Shizuki ordered her to do it.
When Yukime goes Murder the Hypotenuse on Ritsuko in Hell Teacher Nube, she's not exactly happy since she's doing it in a desperate gambit coming after a Breaking Lecture, and repeatedly tells her victim thing like "I'm so sorry", "it's not your fault", and "I wish there was another way to do things!"
Cammy in Street Fighter II V, unlike her regular canon version, she is not only a Technical Pacifist, but also a very devout Catholic, and as such she apologizes each time she lands a punch on her opponents.
Aries of Fairy Tail does this pretty much every fight she's involved in.
Mr. Nice, a minor villain from the Batman: The Animated Series tie-in comic, is not only apologetic, but outright helpful to his victims, even going so far as to give money and his doctor's card to security guards he's tied up and beaten.
Subverted in Nodwick when Artix and Yeager apologize to a villain (after they'd had fun fighting their way through his dungeon, unlike the one they'd just been in that they'd found boring) because Piffany was about to attack him.
In Patoruzú, Patoruzu hits Gaston the Frenchman hard enough to knock him unconscious. Isidoro points out that he may have killed him with his sheer strength. The moralistic Patoruzu is horrified by this and promptly apologizes to the unconscious Gaspar for hitting him so hard. It turns out that Gaspar was faking unconsciousness in order to make Patoruzu feel guilty so he could catch him off-guard.
Ragdoll does this a couple of times in Secret Six.
As seen above, Tintin does this to get a panicky passenger out of the pilot's hair so he can concentrate on his emergency landing.
Blaine in Solar Winds has a tendency to apologize—or at least feel sorry for— any Mooks he has to attack, at the begininning of the story.
The protagonist of You Obey apologizes to the detainee he is interrogating for pushing her on a delicate subject.
As Jaime Lannister in The North Remembers tries to escape out of the White Sword Tower after being put under arrest, he kills Qyburn by jamming his sword up through his spine. As he lays dying, he apologizes and tells him that it was Nothing Personal.
The [Manga/Naruto] fanfic Gender Confusion involves a fight between Hinata and Juugo, wherein both parties are less-than-enthused about fighting at all.
Film - Animated
A very creepy version occurs in Coraline, where the badly-mutilated Other Father is strapped into the mechanical mantis and forced to attack Coraline, mournfully mumbling apologies as the mantis stalks her.
Other Father: Sooo sorry . . . Mother's maaaaaking meeeeee! Don't waaaant to hurrrt youuuu. . .
Calhoun: Look, you're a nice guy, I can't just- Felix: NO MA'AM!! The arcade is depending on us!! Now do your duty, that's an or-*punch*-OWWW!
Film - Live-Action
In Men In Black, the Arquilian battlecruiser that parks over Earth sends a simple message: "Give us the Galaxy or Earth will be destroyed. Sorry."
An example where the person being attacked isn't a villain occurs in The Matrix Reloaded, when Seraph apologizes to Neo before attacking.
In Force 10 From Navarone, Maritza demands that Barnsby hit her to make it appear that he and Mallory attacked her and got away. Barnsby apologizes and hits her weakly. She berates him and orders him to hit her harder. Mallory suddenly punches her hard and knocks her out.
The Princess Bride: "You seem a decent fellow. I hate to kill you." "You seem a decent fellow. I hate to die."
And later, after his fights with Inigo ("Please understand I hold you in the highest respect.") and Fezzig ("I do not envy you the headache you will have when you awake. But for now, rest well and dream of large women.").
Wesley in Wanted was a bit of a nebbish who apologized for everything. After he meets Fox, and balks, asking what his target did to deserve being killed, the next target is apologized to, as Wesley still isn't morally committed even though he's otherwise committed.
An example where both parties were equally neither bad nor good, in the film Highlander, in the battle scene where Connor receives his mortal wound a priest slits the throat of a member of the opposing clan and then quickly offers last rites.
Done traumatically in District 9 when Wikus is forced to shoot a chained-up alien. His hysterical, traumatized reaction is one of our first indications that he's not an outright Villain Protagonist, and that despite his employer's xenophobic propaganda he still views the aliens as people.
The Operative in Serenity. River is also very apologetic after she beats Simon up in order to get to the bridge.
Felipe:(WHACK!) God forgive me. (WHACK!) God forgive me.
Subverted initially by the monk in Dragonheart as he's quoting humorous scripture while (non-fatally) shooting mooks with arrows, then plays it straight when he sees the Big Bad, grunts out "Thou shalt not kill" while trying to fatally shoot him.
Played for laughs in Attack of the Clones when C-3PO's head gets knocked off and is fused to a battle droid's body, forcing him to open fire on the Jedi Knights, him frantically apologizing for every shot fired. (He never lands a single shot)
Carlisle: "I don't relish the thought of killing another creature, even a sadistic one like James."
In Cellular Jessica apologizes to one of the bad guys after she kills him by cutting his brachial artery.
Jessica: "Tenth grade biology. Brachial artery... pumps 30 liters of blood a minute. There's only five in the human body. I'm sorry."
The Amazing Spider-Man : Shortly after being bitten, Peter gets into a completely accidental fight with a subway car full of people. It starts when he rips a woman's shirt off because his hand sticks to the fabric. A couple of guys take a swing at him, but they trigger Peter's spider-sense and he reflexively knocks them to the ground, apologizing each time. A few more people try the same thing and get the same result, apologies and all.
Blazing Saddles: Reverend Johnson prays for forgiveness after attacking one of the bandits with his Bible.
In Star Trek Into Darkness, Scotty apologizes to a security guard while on the USS Vengeance before he opens the airlock to allow Kirk and Khan to enter the ship and let the guard exit the same way.
Layer Cake: A distressed Sidney apologises after he guns down the protagonist.
A violent and disturbing example occurs in the Extended Cut of Alien³ with the prisoner Golic. Already driven mad by the sight of the Xenomorph, he insists that he must see it again after the other in-mates have successfully trapped it in a nuclear storage room, where it can't escape. Another prisoner is guarding the only door, and warns Golic that it will kill him. Golic looks away, mutters an apology... then cuts Arthur's throat with a single slash from another prisoner's shaving razor, babbling panicked apologies as the inmate quickly bleeds out. It's potentially creepier when you consider that Golic appears to exhibit some religious reverence for the creature, and he asks it what to do, making one wonder if perhaps it's controlling or speaking to him somehow, making his apology seem all the more sincere.
In George RR Martin's A Song of Ice and Fire series, there is a successful assassin's guild called The Sorrowful Men, who always apologize to the victim for killing them just before the victim dies.
Varys apologizes profusely to Kevan Lannister after he mortally wounds him with a crossbow, explaining that he had no choice but to kill him to keep the realm unstable and ready for the Targaryens to return.
In Audrey, Wait!, Audrey's mom had to quit Taekwondo because "she was always apologising to the attack dummies".
In Terry Pratchett's The Fifth Elephant, Sybil Vimes automatically says, "I'm terribly sorry!" just as she whacks a guard over the head with an iron bar. This is an interesting counterpoint to her original character, in Guards! Guards!, as an overpowering personality who takes no guff from anyone. In the rest of the series she's far more polite and apologetic, despite taking just as little guff.
In Harry Potter and the Deathly Hallows, Voldemort says "I regret it" when murdering Snape. He might have even meant it too, since he just lost his most capable servant. It's also a very minor version as there was no humanity behind the sentiment.
In Point Blanc, book two of the Alex Rider series, the Gentleman, an assassin, gets his nickname because he always sends flowers to the families of his victims.
Jane Bennet, as represented in Pride and Prejudice and Zombies, has been reported to cradle zombies in her arms, apologizing for dismembering them, even as what remains keeps trying to bite her.
Iella Wesseri's husband, thought to be dead for two years, was found in a prison when the New Republic captured Coruscant. Iella was delighted to have him back, and although he seemed quieter and weaker than he had been before this he was also glad to see her again. Later Iella, being a New Republic Intelligence officer, was assigned to escort an Imperial informant to safety only for her husband to shoot the informant and try to kill her. She shoots her husband, and as he's dying she finds that during his long absence Isard turned him into a Manchurian Agent. Surprisingly, he doesn't say the word "sorry" at all during that, but regret is pretty heavy throughout what he says to her.
Jedi Apprentice has a friend betray Obi-Wan for selfish reasons, though he'd still considered the young Jedi to be a friend. Obi-Wan responds to his apologies with "Save your sorrow. I don't need it."
In the Warhammer 40,000 novel "The First Heretic", part of the Horus Heresy Series, the main protaganist whisper "Forgive me" over the vox channel to a loyal captain during the famous Drop Site Massacre, right afterwords he gave the order to open fire, causing thousands of the loyalists to die within seconds.
In the Mistborn series book Hero of Ages, Marsh tells Sazed, "I wish I understood why I have to kill you. I'm sorry." Then he attacks him.
It turns out this is the real way to use the eponymous Sword of Truth in the Sword of Truth. Holding onto pure anger will get some mileage out of it, but holding onto pure forgiveness will cut through magical defenses. Naturally, true forgiveness is pretty hard to not express to some extent. YMMV on this one, as the first example overlaps with Stockholm Syndrome. It makes sense in context.
Chloe from Darkest Powers is this whenever she accidentally raises the dead.
Lampshaded in The Belgariad, as Durnik the smith apologizes before removing an enemy's helmet and clonking him on the noggin. Belgarath is apparently torn between laughter and confusion. "Excuse me? EXCUSE ME?"
The Dresden Files: Harry Dresden whispers "God forgive me" when he kills Susan, the mother of his child. She had just turned into a full vampire and if he killed her on the altar, the powerful bloodline curse would run through the vampires and end them forever. Susan allows Harry to kill her to save her child from these monsters.
Redwall: Blaggut's last words to Slipp: "You're bad all through, you'll never change, that's why I gotta do this. Sorry, Cap'n!"
Szeth in The Stormlight Archive doesn't want to kill people, but by the rules of his culture he has no will of his own; he has to follow every command of whoever holds his Oathstone, with the exception that he can't give up his Shardblade, or kill himself. And if you have complete control over the world's only regeneratingexpert fighterGravity Master with a sword that can cut through anything...what else are going to do with him? Over time he stops apologizing and comes to hate the people he fights for not being able to kill him.
Live and Let Die - one of Mr. Big's mooks is told to take Felix Leiter out and "hurt him considerably", but the two of them get on well thanks to their mutual love of jazz. The mook, not willing to cross his boss, apologetically hurts Leiter just a little.
Live Action TV
In Smallville, Chloe always apologizes when she is forced to subdue Clark with kryptonite, as shown in Splinter, Hypnosis and Progeny, even under Mind Control with the last case.
In Freak, Clark shouts that he is sorry as he painfully burns a hole in Chloe's chest. He is trying to get a dangerous device planted into her out, and it is under her request.
In Upgrade, Chloe apologizes when she is forced to tranquilize Lois.
The Walking Dead: Shane does this before shooting Otis so he can escape a pack of walkers chasing both of them.
In the first episode of Andromeda, Captain Hunt's Nietzchean crewmate (who practices the species-wide belief of self-interest) sees that Hunt is at an disadvantage. He stands up, apologizes for his impending treachery, and then attacks the captain.
Orwell does this in one of her few action-ish moments(she prefer to work behind the scenes): "Sorry! Sorry." as she tazes a guy in the neck.
The M*A*S*H episode "Dear Sis" centered around Father Mulcahy feeling guilty for punching out a delirious guy so that he could be operated on. Mulcahy's actions would be reasonably justified by the regular morals of planet Earth, especially since the other guy punched him first and Mulcahy decked him in self-defense. And the guy might have died if Mulcahy did nothing. Did the guy, perhaps, feel grateful for this afterward? Of course not.
In the episode "Where No Man Has Gone Before", Kirk pauses to apologize to Gary Mitchell before smashing him with a rock. Mitchell just happens to get back his super-powers in that instant.
And in "Operation - Annihilate!" a whole colony does this: they've been infected by Puppeteer Parasites, and they apologize and beg their victims to run away even as they're attacking.
In "The Man Trap", McCoy says "Lord forgive me," as he kills the Monster of the Week, which had shapeshifted into his ex-girlfriend.
In "Time's Arrow, Part 2" of Star Trek: The Next Generation, Riker says "I just want you to know that I have the utmost respect for the law" to a policeman, then punches him out.
Jack Bauer. For the "You're not evil, but you're in my way - therefore I'm going to incapacitate you rather than torture or kill you" version, anyway.
Tony apologizes right before he smothers Larry Moss.
During the showdown with Crichton in the Farscape episode "Self-Inflicted Wounds," Pathfinder Neeyala remarks, "I have never before released my bristles to kill. Your forgiveness."
In Heroes, Hiro briefly bows and apologizes to Tracy before punching her in the face.
Encouraged in the Rahmens parody educational series The Japanese Tradition episode about dating. If you are forced to fight, you should say "I'm sorry I have to do this" before dealing out justice.
In the Doctor Who episode "Invasion of the Dinosaurs", Sergeant Benton attacks his superior (who's on the wrong side):
General Finch:(with his hand in Benton's face) You'll be court-martialled for this, Sergeant!
Sergeant Benton:(while repeatedly slamming the General against a desk) Yes, sir! Very sorry, sir!
And then later, in the revived series 5 finale, Auton!Rory apologizes desperately to Amy as he's forced to kill her.
The Doctor, in Classic Who, would many times apologize, on the rare occasions when he punched someone, such as the fifth Doctor, in "Warriors of the Deep".
The Tenth Doctor also apologizes all the damn time, and on several occasions "I'm sorry, I'm so, so sorry," meant "I have run out of ideas for how to save you and your victims, so I'm going to kill you now." Obviously does not apply to beings such as Daleks.
The Doctor: "I'm sorry. I'm sooooo sorry. Because you know what I'm going to say to you."
[The Master backs away, almost whimpering, and the Doctor leans in close to his ear]
The Doctor: "I forgive you."
River Song apologizes to a guard for breaking out when it's his first day on the job, using her psychic lipstick on him.
In Prison Break, Scofield does this quite frequently whenever forced to harm good people (often bystanders) to stick to his plans. Justified in that he only starts doing this after witnessing an inmate hang himself, supposedly because Scofield didn't save him from T-Bag.
On Neighbours, Dylan made a point of doing this when he was coerced into an armed robbery. This more than anything convinced Stuart (if not his sergeant) that he was telling the truth, leading him to go undercover to get him exonerated.
The husband on Man Woman Wild always apologizes to the animals he catches before killing them to feed himself and his wife. And thanks them after they're dead, too.
On Criminal Minds, a father and daughter are abducted and he's forced to fight other captives or both of them will be murdered. When the killer ups the stakes and orders him to beat a defeated opponent to death, he has no choice but to comply, moaning "sorry" with every reluctant blow.
During an early episode of Breaking Bad, Walt breaks down crying and apologizing after more-or-less being forced to kill a captive drug dealer. In season 5, Walt apologizes to Mike after fatally shooting him when he realizes the information Mike refused to give him could have been easily gotten from Lydia. Mike just tells him to "Shut the fuck up and let me die in peace.
While it's not verbalized, Jesse's Tears of Remorse when he shoots Gale clearly convey this.
After Hank Schraeder's murder, accomplice Todd Alquist has this to say to the man they spared: "Sorry for your loss".
Leonard Betts, a particularly memorable monster of the week on The X-Files, apologizes every time he kills someone. "I'm sorry, but you have something that I need." That something is always a tumour.
In a second season episode of LOST, Michael apologizes to Ana-Lucia right before fatally shooting her.
Played for Laughs in Angel. Angel is affected by a spell that makes him extremely emotionally sensitive and disinclined towards violence. When he realises he needs to resort to violence to rectify the situation, he very apologetically beats up several people.
Shawn Michaels said "I'm sorry, I love you" to Ric Flair at WrestleMania XXIV just before Shawn used his finishing move and pinned Flair. As a result of losing, Flair had to retire, enhancing causing the emotional impact of the moment.
This later got an Ironic Echo during Shawn's stretcher match against Batista at One Night Stand. The whole thing was essentially a squash match, with Batista finishing it by mouthing "I'm not sorry. I don't love you." Then plastering Shawn with the Batista Bomb.
Destroy The Godmodder: When Minor got turned evil, he tried to stop attacking the AGs. Key word there is tried.
In Warhammer 40,000, the Tau always claim to be apologetic attackers... as they commence orbital bombardment, then use a mix of sterilization, concentration camps, and possibly mind control on their new subjects.
In The Elder Scrolls V: Skyrim, the Subjugated Ghosts in Rannveig's Fast are this, with lines such as "I'm sorry! This isn't what I want!" and "I don't have any choice! I'm sorry!" as they attempt to smash you into a pulp.
Also, the draugr sometimes croak apologies at you in Ancient Nordic.
Fiona Mayfield of Arcana Heart, whose down-forward strong attack is accompanied by a heartfelt "I'm sorry!" as she smacks her opponent up into the air with her BFS.
In the Disgaea series, some of the healer classes shout "Forgive me!" as a battle cry when you have them attack physically. At first glance, demonic healers appearing to feel guilty at attacking enemies is kind of... odd, until Disgaea DS pointed out they are actually fallen angels from Celestia, making them not so different from Flonne ("Whoops, pardon me!"). Old habits die hard, it seems.
Polka in Eternal Sonata will apologize to enemies after hitting them, and one of her opening-battle quotes is something to the effect of "I'm sorry, but I'm in a hurry!"
Dizzy from Guilty Gear has two wings that do most of the attacking for her, and she apologizes for them (and tells them to stop) during battle.
Bridget's intro has him pull a Dynamic Entry and trip his opponent before the fight starts. He then turns, goes all "oops" and apologizes.
In the prologue before the game starts, an alien invasion kills Iji's father and little sister and almost the whole human population, but even after she is transformed into a nanomachine-powered cyborg, she has no desire to kill her attackers and says a grief-stricken "I'm sorry..." when killing an enemy. This gets reversed if you shoot everything you see, however, which makes her yell "Why don't you just DIE!" or similar when shooting them.
During the first battle with Jafar in Kingdom Hearts I, he orders the Genie to attack you. Before every attack, the Genie yells "I'm really sorry about this!" or the equivalent ("Oh please, oh please let me miss!") as well as "Quick, get out of the way!", and if he does hit you, health orbs fly out of his fist to make up for it.
Patrokolos from Soulcalibur V says "I'm sorry" quite often when fighting against his sister Pyrrha, who herself does this a lot due to being manipulated by Tira into becoming a killing machine (and a suitable vessel for Soul Edge).
Despinis from Super Robot Wars Reversal is not just chronically shy, she always says "I'm sorry" before blasting you to smithereens or beating you to a pulp. True to that, when she joins your party in OG Gaiden, she seems to be more proficient at support skills rather than direct combat.
System Shock 2. Some of the "hybrid" enemies will tell you to run or say "sorry" when they were shooting you.
If Mint delivers the final blow in a battle in Tales of Phantasia: "Forgive me, please..."
One of Estelle's opening-battle quotes in Tales of Vesperia is "I'm sorry if I hurt you!"
Kohak takes this role in Tales of Hearts when you fight friendly but Zerom-possessed characters Rage Camellia (Sergeant Morga) and Lonely Veronica (Marin) as bosses.
Susie Evans from Valkyria Chronicles, being a staunch pacifist, will sometimes freeze up and stop moving if you order her to attack someone (regardless of how much AP she has left). She can, however, use Ragnaid on an ally and still move around fine.
That simply doesn't do it enough justice. If ordered to attack someone, she will actually apologize. Depending on your sense of humour, this is either tragic or darkly hilarious.
Susie: Before shooting someone in the head "Sorry if this hurts!"
Susie: Before throwing a grenade "I'm a pacifist!"
Also, one of the enemy lieutenants remarks how the protagonists seem like good people, and he's sorry he has to fight them.
Avril Vent Fleur in Wild ARMs 5 apologizes for the pain she's about to inflict with her attacks.
In Episode I of Xenosaga, one of MOMO's battle end sayings is "I'm sorry, are you okay?" If they collapsed in a shower of blood, they are pretty far from "okay."
Chaos is a more extreme case of this. In certain cases during battle in the second episode, he'll quickly say sorry before attacking. In Episode I, however, he has a pre-battle and battle end quote in which he prays for the enemy's soul.
"Poor lost souls... may you be reborn again anew!"
Most of the Splicers in the series are pretty out of it, but the Pigskin from BioShock 2 occasionally realizes that you're not, in fact, his hated father. He apologizes, but keeps hunting you, because the Saturnine would do horrible things to him if he let you go.
The Handymen from BioShock Infinite will occasionally warn you to run away, and will scream "get off that thing!" before electrocuting the rail you're on. Normally, this would be a simple boast, but it's later revealed that many Handymen were political prisoners charged with pacifism, and turned into war machines.
In Fallout 3, the RoboBrain enemy sometimes acts like this.
There's also Pvt. Jones, a Mister Gutsy robot in Rivet City.
Jones: Sir, you are not authorized to enter the armory. Sir! Please don't make me shoot you, sir!
Litchi also has this line in her winquote against Bang because she thought he was a pervert but didn't know that he was really trying to impress her.
Litchi: I-I'm so sorry! You came out of nowhere, so I thought you were a pervert and smacked you! Are you alright? (He's completely out... but he looks really happy. Odd...)
In general, Litchi also counts. As she is a doctor and a very benevolent one, she really wouldn't like to fight unless the situation is really severe. A lot of her win quotes had her apologizing to her enemies, and in the Arcade Mode, she was clearly sorry for having to force her way through by beating her colleague Tager. She also goes so far as practically apologizing to Platinum if she beats her, or was beaten in Platinum's story. And she also did this to Rachel in Rachel's story if she beat Rachel, apologizing about how she just beat her and still had to stick with NOL against Rachel's suggestion.
By Chronophantasma, she does this even more often. Justified that as much as she's sticking with NOL, she's not very pleased with the prospect of beating those she deemed decent and friends with, but is Forced Into Evil. In fact, she's mostly borderline crying in win quotes to some close friends, like Bang.
Artix Entertainment games have rare occurrences where the heroes fight against someone only to find out after beating them up that they weren't really as bad as the non-player characters who sicced them on them made them think and they apologize to them before deciding to show those non-player characters who's boss for setting them up and using them. A good example is during the cutscene after the hero defeats Lord Ovthedance where he/she apologizes to him for not realizing that the Great Godfather of Soul set him up and conned him/her into doing his dirty work.
Hero: The Great Godfather of Soul's conned me into doing his dirty work! That weasel! Lord Ovthedance: Me glad you realize that. Would have been better if you realize it before you beat Lord Ovthedance down. Hero: Yeah, sorry about that. We've got to get you down to that Dance-off so you can beat that liar for both of us! Lord Ovthedance: Am you kidding? Me am not in the best shape, thanks to some random hero who decided to... Hero: ...I said "I'm sorry".
Bug! has a Mook that turns around and farts at Bug's face! While apologizing with a rather crude "Sorry" or "Sorry, just ate".
SD Gundam G Generation's system that lets you put any non action girl into a mobile suit usually results in this. Tifa, Shekti, and other girls of their kind will apologize their opponent before blasting them up to bits.
In Abe's Exodus, the second Odd World game, the only way to calm down a Mudokan that had been exposed to laughing gas was to give them a good hard slap. Slap them again and they get "angry" and have to be apologized to or they will refuse to listen to any instructions and even slap you (or any other nearby Mudokan) back. If you slap a "sad" Mudokan, you had better apologize fast, or they will let out a pitiful little "no…" and start beating themselves to death with their own hands.
Rival Schools: When initiating a team-up attack as Unmasked!Akira, she shouts "Gomen nasai!" ("I'm sorry!") while she performs the initial hit.
Hamton from Tiny Toons: Defenders of the Universe apologizes when he throws something at a enemy.
Many of the robots in Cosmic Break appologize when making a kill (even when 'killing' trees and lifeless barrels). Mostly the more human ones. Some however like Baltheon invert the trope by laughing.
Dragon Quest VII (AKA Dragon Warrior VII in the States) has a great beginning world that partakes to this. The first dungeon has THREE bosses. A miniboss to enter, a second-in-command, and a world-sector boss. There is no break to heal or save in between the last two. Why does this fit? The World-sector boss is Matilda who only asks you to kill them and free the world-sector. They only defend and the battle just turns into a Tear Jerker with bonus exp.
In Persona 3 Portable, Bonus Boss Theodore is extremely apologetic when he fights the player character. His sister Elizabeth also apologizes occasionally when she hits you, but not nearly as often.
PROXY from Star Wars: The Force Unleashed'' has the "primary programming" directive of killing his master, Starkiller. However, being a very naive droid who literally doesn't understand the concept of death, he treats it like an ordinary task and is otherwise quite friendly toward him. In fact, every time he randomly attacks Starkiller and fails to strike him down, he apologises for it.
In Pokemon Mystery Dungeon Explorers, Grovyle is notably apologetic to the Lake Guardians about stealing the Time Gears, which makes sense considering he's only stealing them to save the world in the first place.
In Blue Planet, the UEF pilots will often comment that they hope their opponent finds peace in death after shooting them down. The fact that they're not the aggressors in the conflict is a major reason for this.
Samara in Mass Effect 2 often says "Find peace in the embrace of the Goddess" to her enemies before she dispatches them. It's most poignant when she says it to Morinth, her daughter.
The Pandora Artillery in Rise of the Reds, which fires neutron shells, has the line "May our children forgive us" as he is about to fire. When selected, he may also voice ethical concerns about using these weapons.
In Civilization V, Isabella will apologize for betraying and declaring war on you.
In the text game Gun Mute, the friendly robot barwoman in the saloon, Juanita, explains that she's been programmed to shoot you on sight. She's such a bad shot that there's no danger of her shooting you, but she still apologises.
In Fire Emblem Awakening, one of Olivia's quotes has her screaming "I'M SORRY" at the enemy whenever she crit-hits them. Or when she's promoted into an Assassin and Lethality activates.
Serah in Final Fantasy XIII-2 tends to apologize to the monsters she just killed. Her partner... not so much.
Noel: I'd say I'm sorry, but I'm not!
a2 ~a due~: The flute player of the orchestra gets at least one moment of this.
Flute player: I- I'm really sorry about hitting you, b- but- but I can't let you hurt my friends!
The 'Fallen' Grace versus Damien battle in El Goonish Shive definitely qualifies. Damien threatens to kill all her friends, she goes Crouching Moron, Hidden Badass on him, rips him to shreds, then reverts to her ordinary personality and apologizes for beating him up, before asking him to surrender. Of course, he DOESN'T, but that's another trope...
In Everyday Heroes, Mr. Mighty has to knock out Iron Jane after she attacks him ... later, he has to knock her out again to prevent her from killing her former boss in revenge.
Explorers Of Souls: Renée when attacking Mel, uttering "No hard feelings, right?" and "I'm just doing my job!". She doesn't actually seem very sorry, though.
Dr. McNinjahas been shown, in a throwaway gag to when he was younger and still working out the kinks in balancing his ninja and doctor roles, apologizing over and over and over to the body of an enemy ninja he'd just murdered.
He does the same thing here when he realizes that the only way to beat Conservation of Ninjutsu is to team up with the single bad guy against all of the good mooks.
Errol of Seekers profusely apologizes to the female Lizaar as he delivers a sound beating to her in a tournament.
Tower of God: Rachel's last words to Baam: "Sorry. You have to die here."
The Order of the Stick. Roy and Belkar are in a gladiator arena in the Empire of Blood (complicated story), and when he sees a peg-legged man threatening Elan with a shiv, he punches him. Before this, however, he apologizes, saying "I just wanted to let you know that this in no way reflects my views on the differently-abled."
Goblins has a villainous example in the form of Psionic Minmax, who apologises to the Kin from his universe that his plans necessitated him to kill her 817 times. That doesn't stop him killing her for the 818th time though.
The Doctor Who game Eye of the TARDIS from the BBC's website involves the Doctor's consciousness being trapped in the TARDIS computer, and the player is charged with the task of defeating virtual avatars of the Doctor's enemies (by jumping on them to destroy them), and gathering energy crystals so that he can escape. The game features David Tennant's voice, as the Doctor says "Sorry, I'm so sorry" to each enemy avatar as it is destroyed. By the time you get to the fourth level, he is saying this as he destroys Daleks.
In the "Fight Day" episode of Idiotsitter, Billie gets back at Gene for punching her in the beginning of the episode by socking her in the face. She is instantly and sincerely apologetic.
Charlie freaks out and apologizes repeatedly to a villain she has just stabbed in KateModern: The Last Work.
In LG 15 The Resistance Chapter 5, Maggie apologizes to a LifesBlood Labs security guard, who thinks she is saying sorry for running away, before kicking him to the floor.
In Worm, Skitter apologizes to the superhero Triumph, after she nearly kills him.
Later, Dinah Alcott, the third most powerful precog on the planet, leaves Skitter several notes. One of them reads "I'm Sorry." Dinah later organizes an attack on Skitter that exposes her civilian identity.
The circumstances of RWBY's White trailer haven't been revealed, but Weiss' expression◊ while fighting the Knight- and her initial reluctance to go on the offensive- strongly implies that she didn't want to do it.
Silverbolt did this to Cheetor several times in a row once in Beast Wars.
Cheetor commented on wanting to return the favor when the argument was made that Silverbolt was "acting in his best interests".
In Frisky Dingo, when Xander Crews and Killface were forced to fight to the death. They had originally agreed to fake it, and figured they'd think of something eventually, but when the audience wasn't buying it, Killface apologized to Xander before biting his ear off, escalating the fight into actual to-the-death territory.
Starfire from Teen Titans is oftentimes an apologetic attacker.
Member of Team Impossible: I wish there was another way.
Member of Team Impossible: Not really, but that's what our lawyer told me to say.
In another episode Ron tries to make himself a better hero by using a cybernetic suit, only for it—and thus his body—to fall under villainous control. Not only do he and Kim apologize as they attack each other, they have a discussion about their relationship and the insecurities that made Ron think this was necessary in the first place while dodging each other's blows.
On The Simpsons, Nelson apologizes as he is forced to attack Drederick Tatum who has been swabbed with "Poindextrose".
In the My Little Pony: Friendship Is Magic episode "The Return of Harmony, Part 2", Fluttershy is ordered to restrain a brainwashed Rainbow Dash, and proceeds to fly up to the sleeping Rainbow and... gently awaken her, then ask "I'm just wondering if it's okay if I hold you down against your will for a little bit." Twilight Sparkle's reaction is predictable.
In the TV version of Redwall, the abbot asks God for forgiveness after attacking an invader.
In He-Man and the Masters of the Universe (2002), a curse cast by King Hsss turns all of the heroes except He-Man and Roboto into Snake-Men, rendering them Brainwashed and Crazy. (Roboto, being a robot, is immune, and Hsss apparently wanted He-Man to suffer more.) When a fight breaks out, Roboto slugs Mekaneck, saying, "My apologies, Mekaneck."
In the Adventure Time episode "I Remember You", Ice King apologizes to Marceline twice after he pushes her.
The song in that episode has a retroactive and heartbreaking example:
"Please forgive me for whatever I do...when I don't remember you..."
Remember those newspaper articles about the Polite Bandits? Two women desperate for drug money but apparently not too enthusiastic about the criminal business would rob people at gunpoint while saying "Please," "Thank you," and "I'm sorry."
These crop up every now and then, and sometimes end up in the news. They vary from genuinely remorseful drug addicts to professional criminals who simply happen to be polite about their business.
Many people who are members of religions that respect animal rights, but who are forced to eat meat due to economic or health conditions, thank and/or apologize to the animal before eating it.
Choi Min-sik, star of Korean film Oldboy is a Buddhist and said a prayer for every live octopus he had to eat during one particularly gross scene.
There was a recent case where a U.S. Serviceman was mugged at gunpoint by three other men... however, upon opening his wallet and finding his military I.D, they returned it to the man, apologized, gave him back his stuff (except his keys...) and thanked him for his service.
A similar urban legend exists about a group of teens who stole a car for a joyride, opened the glove box and realized it belonged to Mr. Rogers, and returned the car with an apologetic note.
Attila Ambrus, a failed Hungarian hockey player, robbed post offices and banks at gunpoint. He would usually thank the teller, even though slightly drunk.
In Norah Vincent's Self-Made Man, she recounts second-hand an anecdote of this sort. The full paragraph is on the quotes page.
Not long ago, there was a bank robber who apologized for frightening an employee. He apologized for scaring her and sat down to talk. She apparently convinced him to convert to Christianity and turn himself in.
Albert DeSalvo committed several (dozen) rapes in which he would apologize to his victims and show concern for their physical safety. Aside from, y'know, the raping bit. This is one reason why some modern profilers feel DeSalvo and the Boston Strangler were two different people, as the Strangler's victims were savaged by the killer.