Redemption Quest

Maybe your character was The Cape (trope), but fell on bad times. Maybe he was an Anti-Hero who made a mistake and went flying off the slippery slope. They could even be a Villain Protagonist or Anti-Villain who is interested in redemption, either because they've kept their standards, or because they've been in conflict with an even worse villain and shown hints that there might be some good left in them after all. Whatever the case may be, the character is in a bad place but wants to do better, and they are granted one final chance to do so, usually in the form of a grand, nearly impossible task.

Maybe they're being asked to prevent The End of the World as We Know It, or to cure The Virus, or to stop the Evil Overlord. They may not be expected to live through this, but if they can pull it off no one can say that they haven't cleared their name, regained their honor, or insured an afterlife in good old Fluffy Cloud Heaven. (That said, you may wind up with a case of Redemption Earns Life instead.)

Sometimes done in a quieter way as Character Development in a non-fantasy setting, where a character is looking to undo a past mistake or wrong to a love one that has haunted them or caused misery for people around them. Also known to happen in Sports Movies, where a character may see one last great year or performance as a redemption of their prior deeds or careers.

A Sub-Trope of Hero's Journey. Usually follows a Heel Realization, Nice Job Breaking It, Hero or someone saying What the Hell, Hero?. Naturally, a staple of The Atoner. An alternative to Redemption Equals Death. Often a result of Go and Sin No More.

Anime and Manga

 * Rurouni Kenshin: Kenshin's quest to protect people and fight for justice without killing is his redemption for all the lives he previously took as an assassin. Both in the anime and manga, (but particularly in the anime, especially filler episodes or arcs whose stories were changed) he encourages other warriors to try to make amends and work towards making a better world rather than commit Seppuku when they fall into similar situations.
 * Fullmetal Alchemist:
 * Edward Elric "I'm sorry Al. This is all my fault. So I promise that no matter what, I'll get you your body back."
 * Hohenheim, in a much longer timescale.

Comic Books

 * Gargoyles: The whole point to Gargoyles: Bad Guys.
 * Blue Devil in Shadowpact is assigned a Redemption Quest by the Catholic Church, to make up for selling his soul for fame in Underworld Unleashed - which led to the death of his friend Marla - and also to try and counter the Family-Unfriendly Aesop of a guy who sold his soul and subsequently gained demonic power being a high-profile superhero.
 * Anti-Venom (Eddie Brock, the original Venom) is on one of these to destroy the Venom Symbiote; and find some peace from the psychotic remnants of Venom locked in his mind from their bonding.
 * Incorruptible, the companion story of Irredeemable has former supervillain Max Damage trying to be a superhero after The Plutonium, the Superman analogue becomes a Fallen Hero.

Film

 * A frequent theme in the Rocky movies. Apollo pursues a rematch with Rocky in the second movie so he can regain any respect he's lost from nearly losing to a bum, Rocky goes for a rematch with Clubber in Rocky 3 to erase the self doubts caused by the dramatic beating he got in their first fight, etc.
 * The Replacements a Keanu Reeves comedy football movie, has this happening to Reeves' character Shane Falco. Falco had notoriously choked in the final game of his college career, and performed miserably in his little time as a pro, so this last chance at the game represents a chance for him to erase that image.
 * Played with in The Wrestler, where what would normally be the subject of Randy "The Ram" Robinson's Redemption Quest in most other sports movies (namely, his big reunion bout with his old sparring nemesis "The Ayatollah") in fact isn't; his real Quest is to redeem himself in the eyes of his estranged daughter and to make a connection with the stripper with whom he has fallen in love.
 * The film The Fisher King has shock jock Jack Lucas (Jeff Bridges) helping the deranged Henry/Parry Sagan (Robin Williams) in getting a love interest and finding the Holy Grail, as a redemption for having inadvertently caused the death of Sagan's wife.
 * The film The Verdict starring Paul Newman as a middle aged, alcoholic lawyer taking a big malpractice case against a rich hospital.
 * The eponymous Mystery Team is out to regain the respect of their community.

Literature

 * In his Backstory, Dragonlance character Lord Soth was given a chance to redeem his soul after becoming a Fallen Hero. At first he leaps at the chance, but turns his back on preventing The End of the World as We Know It to confront his wife about accusations of infidelity.
 * In The Kite Runner, Amir seeks to redeem his past actions towards Hassan by rescuing his friend's son.
 * The Scarlet Pimpernel is Marguerite's quest to atone for unintentionally causing the execution of the Marquis de St. Cyr, one of the French aristocratic fugitives her husband Sir Percy has devoted his life to protecting.
 * The Silver Chair: Aslan assigns Jill the task of finding the lost prince Rilian as her Redemption Quest for causing Eustace to fall off a cliff.
 * Follows Lale's Heel Realization in The Assassins of Tamurin.
 * spends most of the Harry Potter series atoning for by protecting Harry from harm and working as a double agent for both the Death Eaters and the Order.
 * Elizabeth Bathory toward the end of Count and Countess.

Live-Action TV

 * Brimstone: This is the entire premise of the show, where Fallen Hero Ezekiel Stone gets a second shot at life and a way out of Hell if he returns 113 souls that managed to escape.
 * Lost's Michael has a redemption arc in season 4 after in season 2. He manages to
 * Arguably, Caroline's idea to save $250,000 to launch the cupcake business, the driving arc of 2 Broke Girls.

Mythology

 * Heracles had to do twelve of them after killing his family in a fit of madness.
 * Susanowo must make amends after throwing a dead horse (amongst other squicktastic things) at his big sister's court. He brought back the legendary Kusanagi to her. It's not known how much of it was kicking arses and taking names, and how much of it was genuine remorse.

Tabletop RPG

 * Dungeons & Dragons Plothook #309: "The cleric tells you that before he will cast atonement on you, he wants you to do this for him, to prove your remorse is genuine..."
 * This was a suggested method of restoring a character of an alignment-restricted class who broke his code, in earlier editions; the Player's Handbook specifically refers to fallen Rangers having to seek atonement through deeds.
 * Paladins both play it straight and avert it: if one commits a Chaotic act, she loses her powers and must go on a Redemption Quest, but if she commits an Evil act, she loses her powers and no amount of redemption questing will ever bring them back.
 * Before Third Edition. Third Edition made it possible to Atone (via Atonement, as noted above) for committing an Evil act, and toned down the restriction on Chaotic acts so that it only applies for severe breaches of the Paladin's Code or being enough to shift the Paladin away from Lawful Good (both also solvable via Atonement).
 * This is a suggested plot thread for renegade Abyssal Exalts in Exalted. Redeeming the Abyssal Exaltation back into its original Solar form is explicitly possible- just very, very difficult. So difficult, in fact, that any PC who manages it will be, in the canonical setting, the first ever redeemed Abyssal.
 * Vampire: The Masquerade had Golconda, a state where the vampire no longer has the impulse to kill people and only needs minimal blood to live eternally. The exact ways of achieving it have always been left up to the individual Game Master but the general recommendation was to make it an epic quest, throughout which the vampire in question has to feel remorse for her past sins and make amends as best as she can.

Video Games

 * It initially appeared that this sort of redemption was what Athena and the other gods had in mind for Kratos from God of War, but it turns out that wasn't quite the case. They do forgive him. However, it was not forgiveness Kratos wanted, but to forget all the terrible things he had done. Gods do not grant him that. And that is why there are no more Greek myths.
 * The Light Side path of Knights of the Old Republic, after The Reveal.
 * The Light Side path of the entirety of the sequel.
 * The new Prince of Persia from the Sands of Time trilogy strives to redeem himself by undoing the damage he inflicted upon the time-space continuum by releasing the Sands in the beginning of the first game.
 * Thane Krios has spent the last few years killed despicable, evil people in penance for the years he spent as an assassin for first the hanar and then private individuals and organisations. He is also dying of an incurable disease. When he learns of Shepard's mission to take down the Collectors, he signs up immediately, seeing as the best thing to do with what's left of his life.
 * Subverted in Tali's loyalty mission. The Admiralty Board gives her (and Shepard, naturally) the task of reclaiming a quarian ship that has been overrun by geth. If she is killed, the Board promises to drop the charges against her. If she survives and succeeds, she still has to deal with the charges but the act will lend credence to her side. The subversion comes in where the admirals prematurely pronounce her as KIA and one of them suggests exiling her posthumously, anyway. This being a Role-Playing Game, the final decision is left up to Shepard's diplomatic skills.
 * This is effectively Cecil's story arc for the first half of Final Fantasy IV.
 * Red Dead Redemption. John Marston, former outlaw, is sent by Federal agents to hunt down and kill members of his former gang. It seems like a subversion at first because the Federal agents are actually forcing Martson to leave his peaceful retirement on a small farm by kidnapping his wife and son and threatening to jail or kill Marston for his life of crime, but through the game Martson talks about his desire to atone for all the violence he's committed and how much he hates having to keep killing people.
 * And then ultimately subverted at the end when
 * Tarnum from the Heroes of Might and Magic series spends his entire story arc trying to atone for the terrible deeds in his first life that barred him from entering the Barbarian afterlife. He was cursed with immortality and spent a thousand years fighting evil. Tarnum finally achieves redemption in Heroes of Might and Magic IV by guiding the young Waerjak as he unites the remaining barbarian tribes without repeating Tarnum's mistakes. However, when he is offered admittance into the afterlife he desired, Tarnum chooses to stay with his people, having found a new reason to live.

Web Comics

 * Villainous example: the driving force behind all Dimension of Pain stories in Sluggy Freelance is Lord Horribus seeking redemption for letting Torg escape, by hauling Torg's soul back to the demons' dimension for eternal torment.
 * Similar to the Avatar example, in Twokinds, Keith is sent into exile for killing his father (though this was more to keep the father's good name intact by avoiding a trial) and the only way he could return was to bring back the human Grand Templar with him. He succeeds, though mostly by accident (he'd long since befriended Trace when the group discovered he was the missing Grand Templar)

Western Animation

 * Initially inverted on Avatar: The Last Airbender, where Prince Zuko's Evil Overlord father banished him for not being evil enough, with a hopeless Redemption Quest being Zuko's only means of ending that banishment. Zuko's true redemption quest then comes when he realizes how worthless the redemption his father offered is and instead pulls a Heel Face Turn in the third season.
 * This forms the second half of the plot of The Powerpuff Girls Movie.
 * Ed, Edd 'n' Eddy's Big Picture Show is this for Eddy. During the film, he has to confront the fact his rude, self-centered behavior has serious consequences for him and everyone involved, as he nearly drives his friends away. At the end, he admits the only reason he acted like a jerk is because he was trying to emulate his big brother (who horribly abused him) in order to be respected and liked like him (when in reality, they were afraid of him). Upon doing this, the kids forgive him and accept him and his friends after so much strife.

Real Life

 * An important aspect of restorative justice is about an offender making restitution to his victims. Unlike 'ordinary punishment', restorative justice is about making redemption voluntary and (hopefully!) genuine.
 * Michael Vick is a real life example.