Pride goeth before a fall, but Forgiveness goeth before a stand.
"To err is human, to forgive, divine."
— Alexander Pope, An Essay on Criticism
Forgiveness is perhaps the hardest thing anyone can do, because the things that truly need forgiving are usually those that hurt the deepest. Then again, has the offender really earned forgiveness? Do they have to? Or is forgiveness for such a sin even possible? Is there such a thing as an unforgivable sin? And just to complicate things further, who's to say forgiveness is a good thing in this situation, or at all?
So it is that this cornerstone Aesop causes a lot of problems to all involved. Storyteller included.
The necessity of Forgiveness and its effects are all over the Sliding Scale of Cynicism Versus Idealism, while it commonly appears as the best choice, it's not anywhere near universal. It should probably be noted that every major real world religion insists forgiveness is necessary from its practitioners.
The typical aesop is as follows:
Any character with a legitimate grievance who wants Revenge shouldn't exact it. It just perpetuates the Cycle of Revenge and makes them into monsters as bad as their targets. To get true emotional closure, they should forgive the offender.
They shouldn't take revenge... but if they do, it doesn't make them monsters, and is in fact perfectly fine and justified method of gaining Justice. Usually, this story has Anti Heroes or a Complete Monster of a bad guy.
They not only can, but should take revenge. It will not only give them emotional closure, but will be a long overdue public service since the offender is seriously messed up. Besides, the set up for this isn't one of an "escalating" cycle a la The Punisher, but a single, one off deal that may even end it.
In one arc of the Rurouni Kenshin manga and anime, a little boy's big brother dies protecting him from some bad guys. The little boy gets the chance to take revenge by killing one of the bad guys (who is unconscious), but is convinced not to: it wouldn't give him his brother back, and it would destroy him emotionally (basically bullet point 4 above). Instead, he should live a life that would make his brother proud of him, protecting those weaker than himself and not giving in to evil.
In Gundam SEED, after Athrunjoins the good guys, Miriallia overhears a conversation between him and Kira and learns that it was him who killed her boyfriend Tolle. When questioned about how she feels about this, Miriallia just walks away, saying that revenge won't change anything, thus becoming the first character in the show to actually forgive a misguided enemy.
At the end of Mobile Suit Gundam Seed Destiny, Kira offers friendship and an alliance to Shinn Asuka, who has spent a good part of the series trying very hard to kill him. Shinn actually breaks down crying when he realizes that Kira honestly doesn't hold a grudge against him for this, or for anything else he's done.
In another instance Gundam 00, Saji Crossroad follows Aesop 1 and tried his damnedest to get Louise Halevy to follow his footsteps. Unfortunately, Louise ignores him and goes on to exact righteous vengeance on her parents' murderer Nena Trinity. She ends up in effects 4, for a short while until her mentality and moral gets restored by Setsuna's GN Particles, and Saji's persistence
In Naruto taking revenge makes Team Ten and especially Shikamaru grow up and get over their grief (although it's largely motivated by finishing the mission that Asuma died trying to complete). It's Aesop three.
Sasuke on the other hand leans very heavily on Aesop three to the point of wanting to kill his entire home town for the actions of few elders. Tough to say how he'll end up.
Compare with Naruto, who completely forgives Pain, unlike the two above.
Du hast genug gelitten, deshalb vergebe ich dir, auch wenn dir sonst niemand vergeben sollte. You have suffered enough, so I forgive you, even when nobody else will.
In the final episode of Gundam Wing, Lady Une (having since resolved her Split Personality) offers Relena a gun, saying that she's like a body without a soul and letting the girl take revenge for Une murdering her father. Relena pushes the gun aside, saying they need to break the Vicious Cycle.
Earlier in the series, after Heero is duped into killing well-intentioned Alliance leaders, he goes around to their families and likewise offers them a gun. Field Marshall Noventa's widow writes Heero a letter, asking him to stop beating himself up over an honest mistake and encouraging him to think about the future rather than fixating on the past.
In Code Geass, Shirley, having regained her memories that Lelouch is Zero, the man responsible for the death of her father, is once again conflicted about her feelings, until she realizes Lelouch has been fighting by himself "in a world of lies", and forgives him. She tries to get Suzaku to do the same for Lelouch. Tragically, she is fatally wounded by Rolo a short while later, and after declaring her love and forgiveness in an Anguished Declaration of Love, she dies. Tragically ironic in that it has the effect of making Suzaku even more suspicious of Lelouch, who he suspects of doing the deed.
Weed in Ginga Densetsu Weed says in the Grand Finale that friendship and forgiveness should be what would build Ohu up from the devastation Hougen had caused. In fact, his willingness to forgive prompts Gin from pressuring his son to kill Hougen and announces him as the new leader of the pack. So this would mean Weed took option number 1.
Subverted in the case with Kamakiri. Weed says that he would never forgive any dog who would risk others' lives to save their own hides. Kamakiri, however, doesn't give a crap.
In the finale of Kill la Kill, Ryuuko, having defeated her tyrannical and maniacal mother Ragyo and stopped her plot of converting the entire Earth into an incubator for Life Fibers, urges Ragyo to come down with her back to Earth just like the mother and daughter that they are. Unfortunately, Ragyo chooses death instead, destroying herself and spreading her Life Fibers into space.
Luke Skywalker, in the comic Star Wars: Union, had his wedding to Mara Jade interrupted by a rogue Imperial who didn't like the Empire-New Republic peace set up in the Hand of Thrawn duology. Luke coaxed the Imperial into explaining his fears, gently debunked them - and then, once the Imperial was just sad and unhappy rather than violently driven, invited him to the celebration. Luke's like that.
Unsurprisingly,Superman is all about this, from cheerily recommending Metropolis's reform program to various petty criminals he catches to trying to convince supervillains that if they stop being evil, he'll be more than happy to help them out.
His long time science assistant Emil Hamilton started out as a villain and attacked Superman. It helps though that he was basically a nutty scientist pushed over the edge by corporate double-dealing ala Luthor. He was clearly from the beginning the sort of criminal that could be rehabilitated.
Sadly, Hamilton fell into villainy again due to a combination of feeling sidelined as Superman sought aid from other science-minded heroes like Steel and forming a crazy theory that Superman was draining the Sun of energy and bring about the end of life on Earth...4.5 billion years later.
Reed Richards of the Fantastic Four still doesn't really hate Doom (who has tried to kill him a hundred or so times and is constantly making his life hell), mostly feeling miserable and guilty about being the reason for Doom's turn to villainy, even though it wasn't his fault at all. On more than one occasion, a fight between the two has degenerated into Reed begging Doom to reform, and Sue once baldly told Doom that Reed is incapable of holding a grudge, in contrast to Doom, whose entire existence is based around his seething jealous grudge against Reed.
Batwoman: It was one of there peripheral themes. Various Hispanic parents lose their children to The Weeping Woman (a woman who's children were killed and her soul bound to her corpse and the water). After various accusations of racism and implicitly homophobic insults against the Police and Maggie, they stage a mob to get their kids back when the city goes into anarchy. One father is almost killed by gangsters in the Mob, but the Weeping Woman saves him, killing them. The father sees her as the broken soul she is and forgives her, while Maggie, implicitly, does not care about the parent's harassment as they were under duress, but thinks that if she was in the father's position, she wouldn't be able to forgive. In the end, The Weeping Woman saves the children by killing Maro, the man who killed her children to turn her, and who was going to kill them.
Meet the Robinsons deserves a mention from the Arc Words of "Keep moving forward." Considered an inversion because after Goob woke up late thanks to Lewis and causes him to lose the game, his teammates (after beating him up for losing) eventually forgot and forgave him for it. But not Goob, his grudge prevented him from being adopted, and grew up to become The Bowler Hat Guy.
Tia Dalma and Davy Jones continually tear each other up not so much for their past sins as because they can't forgive each other. (Will is deeply moved watching them, and quite possibly inspired to avoid that, despite the wrongs he and Elizabeth had done each in the film, by asking Elizabeth to marry him during the battle; since They Do, they know they can forgive each other.)
Evidently, Jack also forgave Elizabeth for abandoning him to be eaten by the Kraken. He could easily have treated her the same when the Flying Dutchman started to flounder; instead he unhesitatingly rescued her.
The last love scene between Syrena and Philip has him asking her forgiveness for him getting her captured.
In X2: X-Men United, Nightcrawler tells Storm that he didn't hate people who were scared by him when he was working at the circus; he pitied (and this probably implies that he also forgave) them instead.
One of the major themes on the movie, Super 8 such as From the captured alien stopping his Roaring Rampage of Revenge to Alice's father forgiven for the (indirect) death of Joe's mother.
Spider-man goes on a Roaring Rampage of Revenge on Sandman when he discovered he was the one who shot Ben Parker. By the end of the film, Sandman explained that Ben talked him out of taking his car at gunpoint, but his partner caused him to shoot Ben by accident, and deeply regrets it every night. After hearing how regretful and remorseful he is, Spidey forgives him.
After Peter has freed himself of the black suit, Aunt May comes on by and Peter tells his Aunt that he has royally messed things up with his Love Interest and is now lost on what to do. Aunt May tells her nephew that he must to do the hardest thing: forgive himself, and she believes that Peter can do it and that he is a good person still.
From Temple of the Winds, you get the fourth Wizard's Rule: "There is magic in sincere forgiveness; in the forgiveness you give, but more so in the forgiveness you receive."
This valuable lesson is promptly forgotten in subsequent books; or more precisely, the protagonists never attempt to apply it to anyone besides one another.
In The Bible, a woman who had committed adultery, which Jewish law of the time demanded being stoned to death, was brought before Jesus, who was asked what should be done to the woman. Jesus replied, "Let he who is without sin, cast the first stone." Slowly the mob left. Finally, Jesus, who canonically was without sin, didn't throw a stone, and instead sent the woman on her way with the advice, "Go now, and sin no more."
It's present in the Old Testament, as well, most famously with Joseph forgiving his brothers for their past bad treatment of him and selling him into slavery (he points out to them that despite their wicked intentions in doing that, it ended up being a good thing as he became the prime minister of Egypt and was able to save hundreds, including them, from starvation).
According to the 10 commandments, the divine forgiveness is at least 500 times greater than the divine wrath (it said in the commandment about idolatry, that God will punish until the fourth generation, if they continue sinning, but will reward thousands (minimum 2000) of generations, if they don't). It also said somewhere in the Talmud (don't ask me where, the Talmud is a collection of 63 big books), that the measure of the divine forgiveness towards a person is according to the person's readiness to forgive others.
Jesus stated that forgiving others was necessary, otherwise God could not and would not forgive you. This warning was accompanied by a parable where a rich man found that one of his servants owed him around a year's wages. He was about to have the man and his family sold into slavery to pay the debt but when the man begged for time, the rich man forgave the entire debt. Then the servant promptly went out and found a man who owed him a bit under a month's wages and demanded immediate payment. When the third man begged for time to pay, the servant refused and had the third man put in prison. The rich man found out about this and was furious. He summoned the servant, "unforgave" his debt and had the servant put in prison to be tortured until the entire debt was repaid. Fairly clearly an example of the first type.
Máel Dúin of the medieval Irish romance The Voyage of Máel Dúin sets out to sea to kill the pirates who killed his father. He is lost at sea, and after many adventures, a wise hermit directs him back to Ireland with the advice to refrain from revenge, as it is not pleasing to God and the reason for his odyssey. When Máel Dúin has the chance to take revenge, he forgives the pirates.
Alfred, Lord Tennyson's narrative poem "The Voyage of Maeldune" is an adaptation of The Voyage of Máel Dúin. The hermit cites the Cycle of Revenge for why Maeldune should give up his purpose.
In Rick Cook's Limbo System, when humans are held prisoner by aliens, the priest among them discusses philosophy with prisoner aliens. At one point, he says that people must especially love those who have wronged them, and an alien is delighted with the concept: by loving them, you have freed yourself from bondage to them.
In John C. Wright's Titans of Chaos, Amelia is told to speak the word and the universe will be destroyed in Revenge for her killing. It is, it turns out, a Secret Test of Character; when she does not speak, they proclaim she forgives her killers and shows that a human can make correct moral judgments. Later, Quentin manages to nullify a Curse against him for killing Lamia by forgiving her for the injuries she did him.
The Harry Potter series in general has a strong Power of Love and forgiveness Aesop. There's Snape spying for Dumbledore because he was in love with Lily Evans, Narcissa Malfoy lying to Voldemort to protect Draco, Regulus Black trying to destroy a horcrux, Kreacher changing his allegiance when he found out what Regulus did, Percy Weasley realizing the Ministry was corrupt and reuniting with his family ... every antagonist that was more than just a Mook did some form of Heel-Face Turn, aside from the really bad ones.
Someone Else's War: A Muslim boy living in a landlocked country where Christian extremists reign supreme. He loses his entire family and most of his friends to the war. And still he learns how to forgive the people who took them away.
The recurring theme in Battlestar Galactica is that the cycle of revenge between man and machine is perpetuated because neither is capable of forgiveness, season 4 seems to be building up to an alliance between humans and rebel Cylons that may be capable of breaking the cycle. As of the end of the series Roslin forgives Baltar and lets him live (and keeps his terrible secret, no less). Not only does it help her heal emotionally, it also helped cement the rebel Cylon/Colonial alliance and ensure their mutual survival. So all in all, aesop 1 and bullet point 1. Which is surprising considering the tone of the series.
This is shown fully in the end of series 3 of the new Doctor Who. After being imprisoned, humiliated and tormented for a year, not to mention seeing the Earth decimated (literally), the Doctor disarms the Master, corners him and says that the Master knows what happens now. He says "I forgive you".
In Babylon 5, "A Late Delivery From Avalon" Very heartwarmingly shown between David McIntyre "King Arthur" and Delenn. That is the soldier who had fired the shot that killed Dukhat and the Satai who had ordered the Minbari declaration of war. For much of the episode, he believed himself to be Arthur and he needed to return Excalibur to the Lady of the Lake.
A later example involving G'Kar had him declare that, while he could never forgive the Centauri in general for what they had done to the Narn, he could forgive Londo for his (very large) part in it.
"Passing Through Gethsemane": One of Brother Theo's monks (Brother Edward) turns out to have a dark past that he does not remember, and that he only just learned about. A group of people kill Brother Edward, unable to forgive the person he was before (a serial murderer), and the person who actually did the deed is sentenced to "death of personality"—the same punishment inflicted on the person who became Brother Edward. Brother Theo grants forgiveness to Brother Edward as he's dying, and then asks the same of Sheridan of the person who killed Brother Edward, stating that "forgiveness is a hard thing, but something ever to strive for" (emphasis his).
"The Heart of the Matter" by Don Henley.
One of the major themes of the album Lateralus by Tool, especially prominent on "The Grudge" and "The Patient."
In Dorothy L. Sayers' The Emperor Constantine, Constantine discusses with his mother how he had pardoned but not forgiven his enemies before. He realizes that he may not pardon his wife's treachery, but he must forgive her.
It is the forgiveness of the Bishop of Digne that sets Jean Valjean onto his better path near the start of Les Misérables; even though Valjean had just robbed him, the bishop spoke on his behalf to the city guards and got him released, even giving him more silver in order to 'become an honest man'. This becomes a running theme for Valjean throughout the play, and some of his last lines are asking, begging really, his adopted daughter to tell him he's forgiven for his trespasses.
BioShock 2 lets the player practice this with a few characters, notably Grace Holloway (who Sinclair tells you is merely a misguided old lady who loves Eleanor as much as you do) and Stanley Poole (who Eleanor tells you is responsible for you two becoming what you are). Your actions will ultimately influence whether or not Eleanor chooses to save her mother or kill her.
Aribeth can be looking for it by the end of Neverwinter Nights. Of course, events revealed in Hordes of the Underdark indicate that she didn't get it on the material plane, and her quest through the Hells has been a continuation.
Another one from BioWare: This is the end of Carth's arc in Knights of the Old Republic. He gets to have the violent kind of revenge and realizes it brought him no peace at all. Even though he's got a laundry list of reasons to want revenege against the Player Character for his / her actions as Revan, he decides the path of forgiveness is the only way either of them will have peace.
Forgiveness tends to be the Paragon option in Mass Effect 2. A specific example is pushing Garrus towards forgiving Sidonis in his loyalty mission.
Chrono Trigger presents a particularly mixed example when Janus aka Magus offers to join your party. By this point, Janus is responsible for killing Glenn's mentor, permanently shapeshifting Glenn into a frog monster, leading a war against humanity to further his own (noble but misguided) ends, and trying to kill the party. Glenn then steps forward indignantly, Janus says that they must move on, and the player must choose whether he decides to go one-on-one with his hated rival once and for all or let it drop forever.
In Mortal Kombat, of all places, Sub-Zero took Frost as his personal protégé after becoming Grand Master of the Lin Kuei clan, breaking clan tradition to do so. It turned out to be a very bad idea. Frost proved to be violent and undisciplined, and eventuallybetrayed her mentor and tried to kill him. Still, he held no grudge, and refused to kill her, instead freezing her out of mercy and then laying her to rest in a temple, all the while blaming himself for what had happened.
Forgiveness is a theme that is relevant for Presea in Tales of Symphonia. She finds out that Regal was the one who killed her sister Alicia around the same time that she learns that Alicia turned into a monster and begged Regal to kill her. She decides to continue to fight alongside him in spite of that fact, and her personal trial in Welgaia involves her finally letting go of her resentment toward Regal and Altessa, the latter of whom had experimented on her.
Lloyd: I defeated Kratos, the angel, the one who betrayed us. And I forgive Kratos, the hero of the Ancient War, who helped us. That's all.
In Dishonored you can choose whether or not to forgive Daud, the man who assassinated the Empress Jessamine while you were helpless to watch and the crime for which you were framed. On a Low Chaos playthrough he will show remorse and signs of starting to crack under the emotional strain, even commenting that he wants to die so the pain stops. If you choose to engage him, he'll call away his guards, say it's his fight, and actually ask for forgiveness upon defeat (even though he knows it's selfish and he doesn't deserve it). If you do give it to him, both he and the Outsider will be thoroughly astonished. This is unique in the game. Despite bloodless options always being available (and implicitly encouraged by more deaths leading to bleaker endings), the fate of the targets when they aren't outright assassinated is always horrible - perhaps worse than simple death. This is the one point when Corvo's choice is between bloody revenge and compassionate forgiveness.
In Fire Emblem: Blazing Sword, in Lucius and Renault's A support, Renault admits to Lucius that he is the one who killed Lucius's father before his very eyes when he was child, and he falls to his knees in tears and begs Lucius to forgive him. Lucius forgives him.
A common premise for entire stories in children's animation is that a character will commit some accidental offense, such as breaking another character's toy, etc. The other character knows that it was an accident, but is still hurt and can't bring himself/herself to forgive. The character that had the accident may do chores or favors to try to get the character that feels wronged to forgive them. The story ends with the character eventually finding it in their heart to forgive the other character. The original problem may or may not be resolved.
In the story "Forgive Me Not" of PB&J Otter, Pinch accidentally rips Jelly's favorite cape. She keeps doing Jelly's chores, but Jelly won't forgive her. When Jelly accidentally breaks Aunt Nanner's sunglasses, Aunt Nanner forgives her and she realizes that she needs to do the same for Pinch.
In "The Grudge Won't Budge" story of Dragon Tales, Zak is mad at Wheezie for breaking his snoot flute. His anger and unwillingness to forgive is represented by a furry Grudge that actually clings on to him and won't go away until he can bring himself to forgive Wheezie. The Grudge talks to him in a wheedling voice, encouraging him to hold on to his anger and feelings of having been wronged.
In "Playtime at Tolee's" on Ni Hao, Kai-Lan, Rintoo accidentally rips Tolee's painting. Even though he fixes it so that it's as good as new, Tolee won't forgive him. Then, Tolee learns that "When someone says they're sorry / Tell them that's okay so that they won't feel bad."
Katara was the last of the Gaang to forgive Zuko because he had personally hurt her with his betrayal in Ba Sing Se, but after he helped her find her mother's killer, she forgave him. In regards to Katara finding her mother's killer: when she does, she's a heartbeat away from skewering him with rain-bent-into-icicles; when she sees the cowardly shell of a man he (still) is she spares him, but does not forgive him.
Teenage Mutant Ninja Turtles (2012). After the turtles accidently mutate April's father, she declares she doesn't want to see them again. It takes several episodes later when Casey, unaware of the turtles at the time, tells her of an event where he accidentally ruined a friendship to convince her to forgive them after they save her from one of Karai's attacks.
Disney's The Legend of Tarzan has Lady Waltham wanting revenge towards Tarzan and his loved ones over the death of her brother Clayton. Even after she poisons him and had his friends kidnapped, Tarzan still saved her being killed by a pack of leopards. Realizing that someone that good like Tarzan could never kill her brother and saving her life even after what she did to him, Lady Waltham gave Tarzan the antidote and ended her vendetta.