The Villain Must Be Punished

Under most circumstances, the heroes are perfectly content with thwarting a villain's Evil Plan. This is not one of those circumstances; the villain has harmed innocent people, performed all manner of horrible deeds, kicked every dog out there. Simply stopping his plans isn't enough anymore; whether by humiliation, death, or worse, the Big Bad has to actually pay for what he's done.

Compare It's Personal, a common reason why the heroes come to feel this way; and Laser-Guided Karma, where the universe itself does the punishing. Contrast with Karma Houdini. Can sometimes trigger (or just be another point in) a Cycle of Revenge.

Anime and Manga
"Ash: I'm not done with you yet..."
 * Dragon Ball Z:
 * During the Frieza Saga, even as Namek is about to explode, Goku makes it his mission to finish the fight with Frieza against his friends' objections. It isn't enough that he's thwarted Frieza's attempt to use the Dragon Balls for gain immortality; Frieza has to pay for everything he's done, and Goku has to ensure he does so, beating him to a pulp and ripping his pride to shreds before deeming him Not Worth Killing.
 * Brutally Deconstructed during the Cell Saga. After reaching Super Saiyan 2, a rip-roaringly pissed Gohan beats Cell to a pulp, but when given the chance, opts to stand back and let Cell regenerate just so he can continue the beatdown, feeling Cell deserved to suffer as much as possible before he's done. This backfires when Cell, driven to a Villainous Breakdown, attempts to self-destruct and take the Earth with him, forcing Goku to sacrifice himself to stop it.
 * Pokémon: Ash and his friends generally defeat the Team Rocket trio rather easily and let them flee, but there are times where their antics push them past their Rage Breaking Point, after which Ash makes sure that they're not leaving unless he sends them blasting off again.

Comic Books

 * The Killing Joke: Joker invests a lot of time in tormenting Commissioner Gordon, intending to break him and prove that "one bad day" would drive anyone crazy just as it did him. Batman saves him, after which Gordon insists that Batman go after Joker and bring him in without stooping to the Clown's level.
 * Punisher's entire schtick revolves around this. He doesn't want to just lock crooks up; he wants to make them pay for their crimes with their lives.
 * Gotham Central': Harvey Dent in one arc frames Renee Montoya for murder and kidnaps her just as Bruce Wayne pays for her legal defense. He thinks this means she will have to date him as his prisoner. Renee has to point out that he outed her as a gay woman; she respects his virtues as a villain and the good man he used to be, but they're incompatible. Then he threatens her girlfriend, unable to face this logical flaw in his plan; Renee ends up in a gun struggle with him that Batman interrupts. She asks Batman how many times Two-Face will try and murder the ones that she loves as long as he's alive. Batman says the important thing is that Renee didn't become the criminal that Two-Face wanted her to be. Unable to deal with the trauma, Renee resigns from the force and becomes the second Question.

Film

 * In Disney's animated adaptation of Peter Pan, normally Peter is cheerful about facing Hook. He sees their confrontations as a game, something that disturbs Wendy when he pretends to help the crocodile taste some "codfish" as Hook is dangling from a cliff over the water in Skull Rock. Then he finds out that Hook smuggled a bomb into his hideout that nearly killed Tinkerbell, and kidnapped the Darlings as well as the Lost Boys when they were planning to fly to London. After Peter saves Wendy from the plank, he seriously tells Hook, "You're next! This time you've gone too far!" Going after Peter is one thing; nearly killing his friends is another issue altogether.

Literature

 * In the Peter Pan novel, normally the selfish and heartless Peter sees fighting Hook as a game. Then Hook nearly kills Tinkerbell with a poison meant for Peter, and kidnaps the Lost Boys as well as the Darlings. Peter, in his coldest voice, whispers, "Hook or me this time" and goes for one final showdown.

Live-Action TV

 * Angel:
 * In the crossover two-parter "Five-by-Five" and "Sanctuary", different parties host this attitude about Faith, the fugitive Slayer that pulled a Face Heel Turn and helped the Mayor nearly eat the high school graduates in Buffy season three. Wesley, who was her watcher, feels guilty that he was too incompetent to help Faith; he changes his tune after she kidnaps him and beats up Cordelia, pointing out to Angel that Cordelia was an innocent party and Faith can't be trusted. Buffy in the meantime comes to Los Angeles to hunt down Faith after the latter, saying she needs justice. Angel is put in the impossible position of fighting off his ex and at least keeping Faith alive long enough to decide what the right decision would be to do with someone who tried murdering him, tortured his friends, killed a human deputy and has an arrest warrant. When Kate has to arrest Angel for harboring a fugitive, in a case of Reality Ensues, Faith solves the dilemma by turning herself in and surrendering to LAPD.
 * Sweet Fred finds out that her graduate school mentor, Professor Seidel is the one who sent her to another dimension, a traumatic experience that broke her. He did the same to several of his students out of jealousy that they would surpass him. Fred becomes uncharacteristically sadistic, asking the group on if it's better to torture the professor slowly or quickly. Angel says slowly, but he can't let her do that; Wesley is more willing to assist out of guilt. Fred wants to do to Seidel what he did to her: condemn him to another hell dimension for the rest of his life. Gunn ends up doing it, and snaps the professor's neck before exiling him, because he can handle killing a human and keeping his morals intact; he worries what will happen if Fred were to do such a thing, how it would traumatize her further.
 * Buffy the Vampire Slayer:
 * Xander's hatred of Angel first spurs from jealousy; he nurses a crush on Buffy, but Angel becomes Buffy's boyfriend in season two. Things get complicated when Buffy causes Angel to lose his soul and revert to the soulless serial killer vampire he used to be, but she still can't kill him. Xander is not the only one who calls out Buffy for this; Giles wants a piece of Angelus for what he does to Jenny Calendar. When Angelus kidnaps Giles in the season two finale and prepares to cause the apocalypse using his intel under interrogation, even though it will kill him as well, Willow prepares to restore Angel's soul before that happens and asks Xander to relay a message that Buffy should stall Angelus for as long as possible. Xander instead relays this message to Buffy: "Kick his ass." It takes several years for Buffy to learn the truth, and she's furious with Xander long after she and Angel have broken up and he moved to another city. With that said, Buffy also acknowledges that she hesitated on killing Angelus and that she bears some blame.
 * Warren Mears, the Big Bad of Season 6, quickly shows himself to be a vile excuse for a human being, using a Mind Control Device to turn his ex-girlfriend into a Sex Slave, killing her when she snaps out of it and tries to escape, and using magic and time-distorting demons to dupe Buffy into thinking she killed Katrina so she'll take the fall, which nearly succeeds. By the final episodes of the season, he's shot Buffy, nearly killing her, and killed Tara, the latter of which unleashes Dark Willow, who fully intends to kill Warren for it. Dawn and Xander are so disgusted and furious with him that they openly support Willow's intentions; Buffy, meanwhile, preaches Thou Shalt Not Kill, but only because she doesn't want Willow to become a murderer.

Video Games

 * Banjo-Kazooie: After saving Tooty by completing Grunty's sadistic Game Show, Banjo and Kazooie go back home and have a cookout with Bottles and Mumbo Jumbo to celebrate their victory... until Tooty reminds them Grunty escaped and demands they go back and take her out. Only once Grunty is knocked off her tower and trapped under a boulder is Banjo allowed to kick back and relax.

Western Animation

 * In Batman the Animated Series, this happens a few times.
 * "The Man Who Killed Batman". Batman fakes his death and makes it seem that a low-time crook named Sid the Squid offed him, figuring that an apologetic, horrified Sid would lead him to Rupert Thorne since the man offers protection to those who join his mob. When Thorne is about to kill Squid believing he must be a criminal mastermind for killing Batman and surviving a murder attempt from the Joker,.
 * Unlike in the comics where Batman and Robin arrested Tony Zucco after the latter murdered the Graysons in cold blood, Zucco gets away when Dick is a boy, owing to Dick being stupid enough to hunt down the man alone at night, in the city slums, and Batman having to save his ward when Zucco tosses him off a bridge. A decade later, Batman gets a lead on Zucco and says he will bring in the man alone, saying that it's personal. When Robin finds out who Batman is hunting, he is furious and demands to come along and confront Zucco. Robin's arrival ends up timely as Zucco managed to sprain Batman's leg and corner him, and he scares the tar out of his parents' murderer. He ends up not killing Zucco, but admits that it was tempting in the heat of the moment. Batman says that's not why he wanted to arrest Zucco solo; it's that he was terrified when he saw Zucco about to murder a young Dick, and the memory still haunts him. He can't bear anyone wanting to hurt his only child.
 * Teen Titans: Normally, Robin is the one who can't stand Slade and wants to bring him down by any means necessary. When Slade returns in season 4, however, he's gunning for Raven, to Mind Rape and taunts her that her destiny is coming. Raven ends up in uncharacteristic Heroic BSOD as her friends research.