A promise is a promise. (And an agreement is an agreement, and a contract is a contract.) It will bind for whatever term it stated or until whatever condition was required is fulfilled -- forever if neither was — or leave a character The Oath-Breaker forever.
Unless you're let off.
Normally, only the person you made it to can do it, though sometimes the person on whose behalf it was made can — if Sir Jack promised Queen Alisandrine to protect Princess Esmeralda, either the queen or the princess might be able to let him off, provided he accepts it. Oaths made to a god — or sometimes just on the god's name — can be absolved by a religious authority, sometimes. A Magically-Binding Contract can mean that only the attempt can be made, though it still indicates Character Development.
Usually this is a way to indicate development, and a shift from an almost contractual (if not actually contractual) relationship to an open-ended one powered by love, friendship, or trust. There is always drama inherent, particularly if it started out as a Leonine Contract, in that this will demonstrate whether those things really have that power at this point. Or not.
Delicacy may be required to prevent hurt feelings, and if it's lacking, the promise-maker may feel insulted and even rejected. A powerful More Hero Than Thou argument often ensues if the promise-receiver is trying to break the association for the other character's good. Honor may insist that he can not be freed even by the promise-receiver. And insult may be taken in some cultures, where being released from the oath carries the implication that the promise-maker was so flawed that the promise-receiver doesn't want to keep him on.
On the other hand, if the promise-maker lacks scruples, or if it was a Leonine Contract, he may be pretty earnest in efforts to convince the other to give up the promise. Exact Words may be used toward this end as well as evading the spirit of the oath.
If the character received things in return for the promise, things can get interesting. If the thing is no longer possible or applicable, it may merely be a gracious acknowledgement of the fact. However, if the character gets to keep the things anyway, he will often feel guilty. If he doesn't get to keep it, his reaction may vary from fury in high drama, or despair, to a Hilarity Ensues attempt to weasel the promise-receiver out of freeing him.
An exchange of vows often requires mutual agreement, and is very ticklish to bring up. Betrothals are a special case; depending on the culture, it may be only by mutual agreement, only by some flaw, or only by the woman.
There's an old Sonic the Hedgehog fanfic series by Robert Brown and Francis Tolbert (found here) which has an OC called Dorian Lexford. Snively (one of the villains of the story) saves Dorian's life. Being extremely honourable, Dorian chooses to serve Snively until his debt is repaid. Snively eventually chooses to release Dorian from his debt so that Dorian can be with the woman he loves.
In Tangled, Flynn presents his efforts to persuade Rapunzel to release him as a generous offer to release her — she's feeling guilty about abandoning her mother, so he will bring her back without showing her what he promised, and she will give him back what he stole. When that doesn't work, he brings her to the Snuggly Duckling in an attempt to show her the thugs she fears and persuade her thus.
Later, Rapunzel does rescind it, giving him it back before he has completed his promised portion. Gothel intervenes to make her think that he abandoned her immediately.
In Wild Strawberries, Isak has leant his son Evald a significant sum of money, which he insists that he pay back (even though Isak does not need the money, Evald cannot really afford to pay him back and Evald's wife has attempted to dissuade Isak from asking for the money back), which Evald agrees to do. At the end of the film, after Isak's spiritual journey, he attempts to tell Evald to forget about the loan, only for Evald to cut him off and insist that he'll pay him back.
Conan the Destroyer. After Conan frees her, Zula asks to ride with him and serve him. At the end of the movie Princess Jehnna asks Zula to be the captain of her guard. Conan releases her from her oath to him (and grants her permission to take the post) with a nod.
In Corpse Bride, at the end, Emily frees Victor from his accidental promise to her.
In The Lord of the Rings, Denethor releases Pippin, who refuses it and goes to get Gandalf to stop whatever madness Denethor is up to.
This was explicit in the oath, the terms of which were "until my lord release me, or death take me, or the world end."
In L. M. Montgomery's Rainbow Valley, Rosemary and Ellen had promised to stay single together. Rosemary fell in love, and Ellen refused to free her. Later, Ellen fell in love; while she didn't even ask, she told her lover, who asked, and Rosemary nobly agreed to free her and declared she would not tell her love that she was free. Ellen, of course, could not accept her freedom under those conditions. (Fortunately the youngest daughter of Rosemary's love intervened.)
In L. M. Montgomery's Emily Climbs, Emily goes to college after promising not to write any fiction when she is there. After two years, a rich relative took up paying the tuition, and the aunt she promised tells Emily that since it was in return for the tuition, she must release Emily from her promise.
In a P. G. WodehouseMr. Mulliner story, after discussion on escaping engagements, Mr. Mulliner recounts how Mulliners, being honorable, insist that only the woman can break it off, and recounts a story about a nephew trying to persuade his beloved to do so after he discovers what he thinks is evidence of insanity in his family.
In E.D.E.N. Southworth's Ishmael Herman Brudenell told his secret wife, Nora, and her sister that whenever it was better to let the marriage be known, they could tell it. Nevertheless, Nora kept her tongue when his mother confronted her and pled the promise. Her sister berated her for it.
In L. Jagi Lamplighter's Prospero's Daughter trilogy, a Magically-Binding Contract holds the winds obedient to Miranda's flute for a millenium. Mab is always after her to break it and free them. Halfway through the trilogy, Miranda realizes that this sort of slavery may be keeping her from becoming a Sibyl and tells the major winds that if they can figure out a way to keep all the winds from wrecking havoc without it, she will free them from it. At the end, she breaks it to free her brother. Astreus gets the winds to behave despite it.
When Ferdinand appears, he offers Miranda a marriage in name only, so as to technically fulfill her promise to marry him or die a maid, and actually be released.
In Lois McMaster Bujold's Vorkosigan Saga, Miles explains to Elena and her husband that he can't technically free them from their oaths to him, but they can agree to mutually head off on their merry ways.
In The Last Knight, Sir Michael releases Fisk from his obligation to stay with Michael only to have Fisk stay anyway to keep his employer-turned-friend out of trouble.
Maglor: If Manwë and Varda themselves deny the fulfilment of an oath to which we named them in witness, is it not made void?
Maedhros: But how shall our voices reach to Ilúvatar beyond the Circles of the World? And by Ilúvatar we swore in our madness, and called the Everlasting Darkness upon us, if we kept not our word. Who shall release us?
In Julie Kagawa's The Iron Queen, Puck explains to Meghan that offering to release Ash from a vow is like tearing his heart out: it means that she doesn't trust him and never wants to see him again. Even though he knows her actual motive — to protect him from a situation of grave danger to him.
In the Back Story of Dorothy L. Sayers's Lord Peter Wimsey stories, Lord Peter had been engaged before World War I; he had wanted to have a Wartime Wedding but was persuaded out of it on the grounds that he might end up crippled, which would be unfair to her. He released her from the engagement, just in case, and found that meant she was quickly snatched up by an unscrupulous wooer.
In Caroline Stevermer and Patricia C. Wrede's Sorcery & Cecelia, the Marquis begs Kate to release him from the engagement. Aware of the enchantment, she refuses. She is very annoyed when she realizes he did it to convince that the enchantment was working on him.
In 30 Rock, Tracy releases the suddenly very successful Kenneth from his promise to always be there for Tracy. Tracy reveals that when he got big everyone wanted something from him, and he doesn't want to be that person to Kenneth.
In Babylon 5, when Londo rather abruptly tells Morden and hisassociates that he wishes to end their (implied contractual) relationship, Morden rather calmly accepts this, and does some final "settling up with him", demarcating areas of the galaxy where the Centauri were and were not allowed to conquer. Later he seeks and finds a way to reel Londo back in, however.
In MythQuest, a mysterious knight challenges the court of Camelot to a test of their honor. If he lets one of them cut off his head, will they let him do the same? Caradoc accepts, and when Alex, who has taken his place in the story, willingly sets his head upon the bench, the knight is impressed at his courage and honor and releases him.
In Star Trek: Enterprise, T'Pol has an Arranged Marriage waiting for her back on Vulcan, as per Vulcan custom. However, Trip convinces her not to go through with it. Later, when the Enterprise goes to Vulcan to cure T'Pol's mind-meld-induced illness, her mother expects her to settle down with Koss, her husband-to-be. T'Pol is reluctant. However, when Koss promises to use his social standing to save her mother's career in return for T'Pol's hand in marriage. T'Pol agrees. Then her mother dies, and Koss, seeing that T'Pol doesn't want to be married to him and the original condition no longer applies, releases her from her obligation.
In Neverwinter Nights 2 expansion pack Mask of the Betrayer, two siblings offer to fight alongside you if you can find their older sister Kaelyn. When you bring Kaelyn to them, she asks you to release them from the promise as she doesn't want them being in unnecessary danger.
Later on, Tarvek releases Otilia/Von Pinn from her responsibility to watch over Agatha so she can guard Gil instead. Technically he doesn't have the authority to do this yet, but she really wants to accept, so she decides he's close enough.
Heavenly Nostrils opens with the unicorn Marigold granting one wish to Phoebe for freeing her. Phoebe wishes for Marigold to be her friend. Months later, Christmas approaches, and Phoebe stresses over what present to get for Marigold. In the process, she realizes that obligation isn't a good foundation for true friendship—so for her Christmas present, she frees Marigold from the terms of the wish. Marigold replies that she still wants to be Phoebe's friend.
In an episode of The Real Ghostbusters, Egon's uncle visits the team and wants to take Egon with him, reminding Egon that he promised to help him with his own research, and not believing in ghosts. At the end of the episode they prove the existence of ghosts to him, and he directly tells Egon that he releases him from their promise.