This event is essentially a form Heel-Face Turn scenario where a villain decided to become a good guy, though in the case of Villains' Absolution, the wrongdoer would reflect the error in their ways and sees that in spite of how far he/she go in the path of evil, he/she realized that he/she still have the chance to return to the good side.
There are several ways a villain can redeem themselves including:
Snapping out of a possessed or brainwashed state, and deciding to aid the hero who freed them. The villain is a hypnotized, brainwashed or possessed pawn who does not know they are being controlled until they are freed. Grateful to whatever hero freed them, they ally with them. The cyber ninja Cyrax and the lost Edenian queen Sindel from the Mortal Kombat universe are the examples.
Being exposed to a messiah or pure of heart type of hero who helps them see their errors. Usually done with delusional villains, honorable villains, or insecure villains (the wrongdoer can also have all those traits) who believe they are doing right or just want to be loved. The hero reveals to them that their actions are actually causing harm, or tries to comfort them. The individual chooses their desire for righteousness over what they have done, and/or decides the hero had helped them see what they were doing was wrong, and becomes a hero. Prince Zuko is an example.
Choosing honor before evil. An honorable villain decides that their own honor, or the honor of something or someone else, is more important then what they are doing and decide to abandon their evil actions. Often done with supporting antagonists who value the lives of lower-ranking people in an organization such as Boss Wolf.
Becoming friends with someone and decide to help them over being evil, such as Axel who had planned on betraying Organization XIII with Saïx, but over time built a friendship with two other members, Roxas and Xion, and decided he was happier being with them rather than plotting with Saix.
Choosing their family over evil. Done with villains who have families and to care for them. They realize that their actions are actually hurting their spouses, children, siblings, or any other relatives in their family. One example is Darth Vader.
Being memory-wiped or brainwashed into becoming a hero and deciding that they like their new personality and life better then their old one when they inevitably learn the truth. This is the rarest and most controversial form of a villain redeeming themselves since they did not turn good by their own free will and essentially had to be programmed into being good. Reserved only for villains who would normally be Pure Evil under their circumstances, the audience or reader meets them as a hero first, not knowing they are brainwashed or have fake memories. The "hero" does not know this either and is just as horrified as the viewer when they learn the truth about the horrible things they have done or regain their real memories, but they have spent so much time as a hero and living with an artificial good personality that they choose their new life over their former one and become true heroes. This also includes individuals that happened to be robotic villains that were meant/programmed to be the Big Bad's trump card against the heroes, but due to a certain incident, it ended up discovered and fixed by the heroes that he/she meant to destroy. The said individual even later befriended the said heroes without either them or said individual aware with his/her true goal. One famous example is Darth Revan. Another is Professor Pericles; although he did turn good, it was only in an alternate reality and didn't do out of the goodness of his own heart.
Betrayed by their fellow villainous allies/bosses, which made them choose to turn to the good side. After they antagonize the hero and their deed succeeds, their allies/bosses dump them or try to kill them straight away; either way, the said villain escapes. Having seen the error of their ways (and in the worst case, hunted down by the big bad or their former ally which left them no option but to join the heroes to survive), they choose to turn to the good side by joining forces with heroes. Discord is an example.
Retiring from being a villain and realizing that living as a good guy is more better than his previous life as evil-doers. Megamind and Professor Badlam are good examples.
Learning the lesson of being evil from other villain (usually a Necessary Evil, a Monger or, in the worst of cases, a Pure Evil) In other words, they experience a case of "getting a taste of your own medicine," which leads them to understand that what they are doing is very bad and they feel horrified, disgusted and terribly bad for the actions of the latter villain and try to redeem himself/herself and fight against him/her (a similar but somewhat different to a case of Evil Vs. Evil). In the end of the battle (usually in the end of the very battle/episode/movie or in sequels), he or she will try to join the heroes and search for the pardon to everyone they had become enemies. Shadow the Hedgehog, Lucy, and Selina are good examples.
Simply stopping being evil: There are rare cases where, though they have no real reason, a villain can just decide to stop being evil. Perhaps they tire of it or have successfully completed their goals and have no reason to antagonize anyone anymore. Some of these villains may not be remorseful like other redeemed villains, and instead are proud of what they have done but simply have "retired" from villainy. A good example is the Hatbox Ghost.
IMPORTANT: If the villain is currently in an On & Off status, do not add them unless they stayed good right up to the very end of the story. Also, do not include villains who have done a few honorable/heroic actions, then gone back to their villainous ways afterwards. Additionally, Pure Evil villains have no chance of any redemption, no matter the circumstances. Likewise, it is impossible for a redeemed villain to revert back to their evil ways unless they are brainwashed by another villain (or villains).
Cartoons, Manga and Anime
Sunset Shimmer: After Twilight Sparkle and her human world friends used the elements in them to defeat Sunset Shimmer, changed back from a demon into normal, she immediantly shed tears and apologizes for her actions. Later, Sunset Shimmer implored the human Twilight Sparkle to do the same after the latter's freak accident that turned her into violent and destructive being called Midnight Sparkle.
Chirn: As soon Chirin invaded his childhood farm, he saw a lamb that was like him when he was young and his mother saving him. He then had some second thoughts, but the wolf did had the same beliefs, so Chirin stopped him, saving the sheep for he remembered he's the wolf who killed his mother. Sadly, in spite of his redemption, Chirin's training that resulting his transformation into a monstrous being that he became has condemned into a half-life for the rest of his life (his childhood farm inhabitants exiled him for how monstrous he had become).
Terra: After the Teen Titans revealed to survive her attacks, Slade revealed his true color by abused her and even showed lack of concern with her well-being, pressured her enough to went against him.
Dark Heart: When Dark Heart was attacking the Care Bears, he hit Christy as well, and he started to feel remorse since she save him from drowning.
The Grinch: His in How the Grinch Stole Christmasis no doubt one of the most famous absolution in history. After the Whos in Who-Ville sang without the presents, he began to realize that Christmas isn't about presents with the guilt for his evil act hurt him so much that it feels as if his heart become larger.
Prince Zuko: After some time in the fire palace and learned that how Fire Nation become monstrous forces revealed to be rooted from Sozin's betrayal against Avatar Roku (whom later reincarnated into Aang), Zuko realizes that he should join the Avatar gang, though he succeed to gain their trust once he aid Katara to confront her mother's killer.
Mai and Ty Lee: Mai went against Azula for the love of Zuko and Ty Lee went against Azula for Mai, inadvertly exposed the fact that whatever bond that they share with Azula all this time was fake.
Discord: Because Fluttershy called Discord her friend for making her house lively, Discord felt good. But then started to abuse it for his advantage, but then Fluttershy started to snap, but Discord didn't care for he's the spirit of chaos. But then he realizes that he'll lose the only friend he ever made, so he made everything back to normal.
Starlight Glimmer: Twilight Sparkle brought Starlight Glimmer into the terrible future after another failed attempt to restore the past, but Starlight was persuasive for cutie marks costed Starlight her only friendship. So Twilight offered Starlight her friendship.
Jinx: Kid Flash charmed her saying, she does not have to be the bad guy.
Kraehe: Kraehe took a glimpse of her past and discovers who she really is: not the daughter of the Raven, but an ordinary girl. With that she lost her Kraehe side and permanently stayed as Rue for good.
Lord Business: Finn tells Business that people's creativeness are wonderful, he's one of the greatest people who ever lived and he does not have to be the bad guy whom limited everyone's creativeness.
Iago: In The Return of Jafar, Iago got fed up with Jafar's abuse and joins the good guys for his own gain, and eventually stars to actually warm up to them, and eventuaully redeems himself by kicking Jafar's black lamp into molten lava, destroying him forever.
Scalawag and Igor: After Pinocchio saves Scalawag and Igor from the Pike, they start to have second thoughts about selling him to Puppetino and the Emperor of the Night.
Peridot: In Steven Universe episode "Message Received", she joins the Crystal Gems by insulting Yellow Diamond and calling her "clod" after refused to destroy the Earth with the Cluster.
Darth Vader: His' no doubt one of the most famous absolutions in history. When his son, Luke Skywalker was being tortured by Emperor Palpatine, Darth Vader sacrificed himself to save Luke by throwing Palpatine into the pit. As he was dying, Vader asked Luke to remove his mask so he can see his face for the first and the last time.
Winter Soldier (Marvel Cinematic Universe): Having this once he remembered his past self and saved Steve Rogers from drowning, and set out to destroyed HYDRA's assets that used to brainwash him. Unfortunately, returned to the good side by his own terms is not enough to retain his good self due to HYDRA has arranged a fail-safe programming in his brainwash procedure where he would revert to his brainwashed self for limited amount of time via trigger words.
Ebenezer Scrooge: His' no doubt one of the most famous absolutions in history. After the visits from the first two spirits and seen what the Ghost of Christmas Yet to Come shown what will his future be like, Scrooge apologizes for all the wrong he did and he will change and honor Christmas in his heart for the rest of his life.
The Once-Ler: The Once-Ler realizes the errors of his ways (a little too late) when he chops down the last Traffula Tree of them all.
[crying] I-I'm sorry. I'm so sorry. I didn't know there was another way.
~ Discord after realizing he'll lose the only friend he ever made if he doesn't turn everything back to normal.
(Twilight Sparkle: Starlight, you're right! I don't know what you went through! But I do know you can't do this! I've seen where this leads, and so have you!) Starlight Glimmer: I only saw what you showed me! Who knows what'll really happen? (Twilight Sparkle: I've seen it a dozen times! Things don't turn out well in Equestria without my friends!) Starlight Glimmer: Ugh! What's so special about your friends?! How can a group of ponies that are so different be so important?! (Twilight Sparkle: The differences between me and my friends are the very things that make our friendship strong!) Starlight Glimmer: I thought Sunburst and I were the same. But we turned out different, and it tore our friendship apart! (Twilight Sparkle: So try again! Make new friends! And if something that you can't control happens that changes things, work through it together! That's what friendship is! And it's not just my friendships that are important to Equestria! Everypony's are! When yours ended, it led us here. But just imagine all the others that are out there waiting for you if you just give them a chance!) Starlight Glimmer: How do I know they won't all end the same way? (Twilight Sparkle: I guess it's up to you to make sure they don't.)
Darth Vader: Luke... help me take this mask off. (Luke: But you'll die.) Darth Vader: Nothing... can stop that now. Just for once... let me... look on you with my *own* eyes. [Luke takes off Darth Vader's mask one piece at a time. Underneath, Luke sees the face of a pale, scarred, bald-headed, old man - his father, Anakin. Anakin sadly looks at Luke but then gives a tired smile] Anakin: Now... go, my son. Leave me. (Luke: No. You're coming with me. I'll not leave you here, I've got to save you.) Anakin: You already... have, Luke. You were right. You were right about me. Tell your sister... you were right. [Anakin smiles and his eyes begin to droop slumps down in death while giving one last dying breath] (Luke: Father... I won't leave you.)
No, Spirit! Oh no, no! Spirit! Hear me. I am not the man I was. I will not be the man I must have been but for this intercourse. Why show me this, if I am past all hope? Good Spirit, Your nature intercedes for me, and pities me. Assure me that I yet may change these shadows you have shown me, by an altered life. I will honour Christmas in my heart, and try to keep it all the year. I will live in the Past, the Present, and the Future. The Spirits of all Three shall strive within me. I will not shut out the lessons that they teach. Oh, tell me I may sponge away the writing on this stone!
That there, that's me? Then I... after all this. I'm not the Raven's daughter. I had a mother. I had a father. I'm a normal human being?
~ Kraehe discovering the truth that she is not the Raven's daughter and changes into Rue for good
You don't have to be the bad guy. You are the most talented, most interesting, and most extraordinary person in the universe. And you are capable of amazing things. Because you are the Special. And so am I. And so is everyone. The prophecy is made up, but it's also true. It's about all of us. Right now, it's about you. And you... still... can change everything.