"You have heard that it was said, 'An eye for an eye and a tooth for a tooth.' But I say to you, Do not resist one who is evil. But if any one strikes you on the right cheek, turn to him the other also; and if any one would sue you and take your coat, let him have your cloak as well; and if any one forces you to go one mile, go with him two miles."
Dr. Tenma in Monster seems to hold this attitude in general, and he eventually saves the life of the main villain, knowing full well what he's done.
Bleach: After being brutally bullied by Loly and Menoly for stealing Aizen's attention, Orihime doesn't hesitate to heal Loly and Menoly when they're savaged by Grimmjow. This act freaks out Loly and leaves her thinking Orihime is a monster. She still tries to attack Orihime later, and forces the much more confused Menoly to help, and is again protected by Orihime. In the end, all Loly can do is repay Orihime by trying to protect her from Yammy.
Keitaro in Love Hina seems to do this a lot to all the girls (except Shinobu). In fact it might be fairly common in Unwanted Harem shows.
Much of Naruto's plot ends up like this. Konoha ninja kills Nagato's parents, who wreaks his revenge on Konoha, and is then hunted down by Naruto... who ends up understanding the whole mess and decides not to kill him back, preventing a Cycle of Revenge. He commits suicide anyway by bringing everyone he killed back to life.
In One Piece, Luffy's first fight against Bellamy. The second fight, taking place after Bellamy attacks and robs people Luffy had befriended, is another matter.
In Angel Densetsu when Ikuno beats Kitano within an inch of his life because of a promise she made to a boy, he kept rising until the boy told her to stop out of grief. Upon being told by Ikuno that Its All My Fault that she beats him, he promptly collapses. Why? Because he thinks he made her so angry that he deserved every punch and kicks Ikuno threw at him. He collapses in relief because that meant their friendship would now not be in trouble as he didn't do anything wrong. My God...
Inverted and done half-literally in an episode of Tenchi Muyo!: Ayeka slaps Ryoko across the right cheek, Ryoko in turn slaps Ayeka across both cheeks.
Yukiteru Amano in Mirai Nikki is infamous for this. The most notable instance is when his dad tries to kill him by breaking his cell phone (though he wasn't aware of the effect and was trying to pay off a debt), takes Yuki's parachute to escape from a burning building, and kills Yuki's mom within the course of one episode. After said dad offers to turn himself in, Yuki's willing to forgive him for all of this. However, Slipping a Mickey and keeping him tied to a chair for a week didn't go over so well with him, but even then, he still forgives Yuno for it later.
It should be noted, however, that Yukiteru does not turn his cheek out of kindness, but rather forgives easily because of his desperate need for affection. Remember, this kid did not have a single friend until he was 14 years old, and that was after he was thrown in a bloody supernatural Battle Royale. It's no wonder he clings to Yuno the way he does.
"A prince forgets the trespasses against him, no matter how terrible. He sacrifices for others, even to the expense of his soul. He forgives until he forfeits breath. He is strong, he is compassionate, and the sum of these things makes him complete... a prince I am and a prince I will be."
Subverted in the 1992 sci-fi movie Freejack, where a nun who helped the hero is being slapped around by corporate goon Mr. Michellete.
Nun The Good Lord always says to turn the other cheek.
She kicks Michellete in the groin, making him double over in agony.
Nun: But He never had to deal with dickheads like you.
In Princess Protection Program, Rosie does this to the Alpha Bitch who just humiliated her, calling it the responsibility of a princess. Carter, on the other hand, points out that she is not a princess and dumps a cone of frozen yogurt on the head of said Alpha Bitch's accomplice.
Another explanation of "turn the other cheek": if a man considered someone to be inferior and he decided to strike him, he'd use the back of his hand; if he considered him equal, he'd use his palm. Basically Jesus was saying that if someone gave you a backhander, turn the other cheek to force him to use his palm.
There is also the interpretation that offering someone the chance to slap you again is a way of showing them that the original insult didn't work, and the slapper has failed in his attempt to embarrass the slappee. As this is usually the fastest way to take the wind out of a bully's sails, turning the other cheek is probably a much better idea than slapping back. Certain Christians interpret this as an endorsement of nonviolent resistance (i.e. civil disobedience).
Another facet to this: In that period, the left hand was still looked upon as unclean, and one could only slap anyone, even the lowest of the low, using the right hand. Turning one's other cheek was essentially to dare them to slap you using the unclean hand, which, being unthinkable, left only one other option, to take it as a dare to backhand the victim, which arguably would be just as big of a shame tainting the aggressor if he "accepted" the unspoken dare. It was essentially a wordless taunt of "go ahead and hit me again. Show everyone watching what a cruel monster you are." So in some regard it's simultaneously an endorsement of nonviolent resistance/civil disobedience and a display of being a Badass Pacifist. Cool!
There are possibly elements of peaceful protest against the Romans in the words written in the New Testament. For example, a Roman soldier can conscript a civilian to carry things for one mile—no more. Carrying beyond one mile can get the soldier in trouble.
A similar sentiment is expressed by the writer of the Book of Proverbs, "If your enemy is hungry, give him bread to eat, and if he is thirsty, give him water to drink, for you will heap burning coals on his headnote this doesn't mean hurt the guy, this refers to the ancient practice of carrying coal in one's hat to keep warm on cold days, and the LORD will reward you." Proverbs 25:21-22.
The Bishop of Digne at the beginning of Les Misérables. Jean Valjean has stolen his silver, and when the police catch him and bring him to the bishop, he confirms Valjean's story that it was a voluntary gift, and adds his even more valuable candlesticks on top of the silver. True to trope, Valjean does a Heel-Face Turn as consequence. Valjean then does the same for Inspector Javert, but Javert can't handle it and commits suicide.
Arthur of the Britons had a monk attempting to convert the Celts to Christianity who did this literally to one of the warlords.
Harry Potter, after being bullied and berated all his school life by Draco Malfoy, Harry proceeds to save his arch-rival when he was about to be burned to death in the Room of Requirement. Harry saves Dudley's life at the beginning of the fifth book. It doesn't even endear him to the Dursleys because they don't understand what happened and naturally blame Harry. Much later, it's revealed that Dudley, at least, is properly grateful.
In Dan Abnett's Gaunt's Ghosts novel Ghostmaker, Major Rawne attacks Gaunt in the field, intending to make it look as if he died in the fight. Gaunt knocks him unconscious and then, in spite of his own wounds, carries him to safety. This did not cure Rawne's resentment, but after a latter situation where Rawne weighs killing him and does not, Rawne does not try to kill him again.
Parodied in the P. G. Wodehouse short story "The Exit of Battling Billson", where a boxer converts to Christianity and decides to apply this philosophy during a match - fortunately for the characters betting on him, he didn't fully understand the meaning of the phrase. After being hit on both cheeks, he thought he had done what was necessary and proceeded to beat his opponent easily.
It didn't work in a Harry Turtledove story where Britain had been conquered and after some tough fighting the Germans had defeated the British Army in India. Non-violent protest proved not to work so well when attempted with an occupying power whose officers are willing to order the machine gunning of your protest march and whose superior officers and government regard that as a fine method to deal with civil disturbance.
The second variation is played with in Discworld's Small Gods. When the god Om gets his powers back, he and Brutha have a minor disagreement over some new laws. Om comments on how he can simply blast Brutha into a little smear on the floor, and Brutha cheerfully agrees that he could, couldn't he? And how Brutha would have absolutely no way of defending himself, whatsoever. Om grumbles that it's not right for someone to use defenselessness as a defense.
This Zen parable - a thief entered the house of a priest who was meditating and threatens him, the priest tells him where the money is, asks him to leave enough for the priest to pay taxes and makes sure the thief thanks him when he leaves. A few days later the thief is arrested, but when the police ask the priest to testify against him, the priest tells them that he gave the thief the money and the thief thanked him. The thief still goes to prison, but when his sentence is over he comes back to learn Zen under the priest.
Simon does this to Jayne in Firefly a few times, which unnerves Jayne more than a direct threat.
Most epically, when Simon and River reveal they know that Jayne tried to sell them out to the Alliance. Jayne was still probably recuperating from getting the crap scared out of him after Mal's threat to space him over the misdeed.
The pilot episode has Mal selling his cargo to Patience, who shot him the last time they met. He also seems completely baffled as to why the rest of the crew would find the incident relevant.
Wash: Didn't she shoot you one time?
Mal: Everybody's makin' a fuss.
The Doctor forgiving the Master at the end of the Doctor Who episode "Last of the Time Lords".
Torchwood's Captain Jack Harkness also follows the Doctor's example.
The Risans in Star Trek take this to a scary level. Based on one episode of Deep Space Nine, terrorism is apparently okay to them so long as the terrorists are enjoying themselves.
Byron the leader of the telepath community that moved onto Babylon 5 used this against a group of anti-telepath bigots, asking one of them to repeatedly punch him in the face and then asking if it made him feel any better. It unnerved the bigots into leaving.
Played for laughs in an episode of Mash, when Father Mulcahey gets bumped on the backside by the jeep of a visiting general. Said general offers an apology, and Mulcahey replies with the trope title.
Ferrovius in Androcles and the Lion allows Lentulus to strike him on the other cheek so he can demonstrate that he is a true Christian. He then seizes Lentulus and asks him to turn the other cheek when he strikes him.
Darcsens from Valkyria Chronicles tend to stick to this whenever anyone is persecuting them, with only few, like Zeri, trying to pro-actively fight against all the racism leveled against his people. Dahau, Zig and the Calamity Raven are also included aside from Zeri.
Over the course of his life, Gulcasa has been betrayed by the people most important to him overand overand over. It never stops him from continuing to trust even people who clearly don't deserve it, and no matter how he's been betrayed, he hates fighting his former friends and refuses to kill them. In Yggdra Unison, one of the few games where he and Nessiah actually come face to face after the latter breaks ties with the Imperial Army, they still banter and tease each other amiably, and you even have the option of bringing Nessiah back into the fold (although that last bit strays into another trope just a little).
Specifically and childishly averted by Taiga in Duel Savior Destiny. He says that if someone slaps him, he'd tape a thumbtack to his other cheek. This sums up his Slap-Slap-Kiss relationship with Lily rather well.
An episode of Moral Orel is titled "Turn the Other Cheek." After listening to a children's song with that title all night, Orel gets it in his head that he should turn the other cheek at every opportunity. The school bully beats Orel repeatedly until his father tells him that he should be doing the exact opposite. Hilarity Ensues again when Orel preemptively attacks at every possible threat of force, even when his best friend Doughty throws rock in Rock, Paper, Scissors.
In season 3, Katara has a chance to confront her mother's killer and becomes consumed for a desire for revenge. Aang urges Katara to do this; in the end, though she nearly ends up killing the man, she refuses. Subverted, though; Katara explains that it wasn't an act of forgiveness, but disgust at what a pathetic person he was.
Katara: I didn't forgive him — I'll never forgive him...
She is, however, inspired to forgive Zuko (who helped her track down her mother's killer), finally forgiving him for his betrayal in Ba Sing Se.
Parodied in the American Dad! episode Rapture's Delight, in which Stan slaps Jesus, who turns the other cheek... and is slapped again.
Jesus: Ow. My other cheek.
Jem often gets called out on this by some fans. Throughout the course of the series, The Misfits have put Jem and the Holograms in situations where where the latter group could have been killed, but Jerrica / Jem never calls the police (she likely had her reasons...).
The one time Eric Raymond got arrested he was released the next day, citing that lawyers can practically do anything you pay them enough. Chances are even if Jem did have the Misfits arrested Eric would have them out in no time flat. What's more infuriating is that the one time they actually were arrested, in KJEM, they weren't responsible.
Jackie Robinson. In order to be accepted into the MLB, he had two prove two things: he's a great baseball player, and a fine gentleman. In other words, he had to have the guts to not fight back when someone hurt him because of his race, and not let loose any sort of curse when someone cursed at him because of his race.
Mohandas Gandhi and Martin Luther King Jr. are both famous for practicing nonviolent resistance against oppressors. While this didn't make the people that oppressed them pull a Heel-Face Turn, it allowed everyone else to see a clear moral contrast between the peaceful protesters and their barbaric tormentors, which drastically swayed public opinion in their favor.
It didn't work for Nelson Mandela in South Africa. When Mandela realised this, he moved to Plan B, sabotaging industrial targets, making sure nobody got hurt. Plan C was to be active resistance against the military, although he was imprisoned before that came to pass.
Ditto with Burma: the monks are pretty much dead now and Burma is the North Korea of Southeast Asia now.
On one occasion it was reported to him that a man had been stealing from his store of winter's firewood, and he was urged to punish him. "I will soon put a stop to that bad practice," said the governor sternly. He sent for the offender. "You have a large family," he said to the offending culprit, "and I have a large magazine of wood; come as often as you please, and take as much of it as you need to make your dwelling comfortable." Then turning to his accusers, he said: "Now I defy him to steal any more of my firewood."