This is basically the trope that sets in motion Mashiro's persistence to become a mangaka in Bakuman。. A promise made in Chapter 1 between him and Azuki,that when he and Takagi get an anime from their manga and Azuki voice-acts the heroine, she and Mashiro will get married.
Utena invokes The Promise in her vow to save Anthy in Revolutionary Girl Utena. Even when she ultimately fails, her valiant attempt leads to Anthy freeing herself to go in search of her fallen hero(ine).
In the Soul Society arc, Ichigo will save Rukia... whether she likes it or not.
During the Arrancar Arc, Ichigo vows to Orihime that "next time... I'll definitely protect you!" Later, he tells her "Don't worry. I'm definitely going to win." This promise is so strong that when Ulquiorra brings him to the verge of death, he is resurrected as an insanely powerful hollow obsessed with protecting Orihime - and only Orihime.
Keitaro holds strongly to his 15-year-old promise to get into Tokyo University for/with a nearly-forgotten girl in Love Hina. He also made a similar promise to forever be with his adoptive sister, which she does indeed dramatically call him on in the OVA sequel, Love Hina Again. The concept of promises also is the main theme of the episode about the Robot Girl Moe.
Both Lottie and Sara in Soukou No Strain promised to become Reasoners and see their brothers again. One brother kills the other before either can reunite.
In Ranma ½, these promises cropping up out of nowhere are common plot elements - Ukyo has at least two with Ranma, Kodachi has one with her rival Asuka, and Ranma has several that he doesn't even know about until they're called.
Naruto is full of "promises of a lifetime"... some more successfully fulfilled than others. The most notable case is Naruto's promise to Sakura to return with Sasuke. The episode after the mission to do this was actually called "The Promise That Could Not Be Kept." Though, he renews his promise and it's still his most important reason to fight, alongside protecting his friends.
Another plot relevant promise is Sasuke promising to avenge his family by killing his brother. Once he succeeds he instantly makes a new one: Destroying Konoha. Obviously that guy needs someone to kill.
Kakashi promised Obito that he would look after Rin. It would seem he failed. The Not Quite Dead Obito witnesses Kakashi actually killing Rin, contributing to his change into Tobi
Vandread's Hibiki made the casual promise to come to Dita's room. Though hardly a big thing to promise, this haunts him throughout the entire second season.
They way they talk about it makes it seem like something else...
In the Battle City arc of Yu-Gi-Oh!, Jounouchi's/Joey's major motivation is his promise to duel with Yugi and get back his Red-Eyes Black Dragon card.
Elfen Lied plays around with this in the scene where the villainous Bando, rescued by Mayu earlier in the series and feeling indebted, promises to save her once if she winds in trouble. Mayu is forced to cash in this promise not even a minute later, when Bando himself attacks her.
But when she calls for his help again, he shows up in minutes and knocks the stuffing out of the man sexually assaulting her.
A second example is Kouta promising to meet Lucy back at the stone on the last day of the festival.
In Digimon Adventure 02, Ken promises to Wormmon that he won't betray his essential nature — in essence, that he'll stay kind and gentle — when he first meets him as a child. Flash-forward to a few years, More than Mind Control, and some heavy psychological trauma later, however, and he's the Digimon Kaiser. He does eventually keep his promise, though. Kinda.
In the previous season, Takeru promises to Sora that he'd protect Hikari. A promise which he still takes rather seriously in Digimon Adventure 02, as he is seen putting himself protectively in front of Hikari (episode 3), seemed angry at himself for accidentally leaving her stranded in the Digital World (episode 7), and doggedly searched for her when she was taken by the Dark Ocean (episode 13).
Super Robot Wars has this: Kyosuke made a promise to Lamia that he'd kill her if she ever loses her mind ("If you ever lose your mind, don't worry. I'll destroy you myself"). He did get his time to try and fulfill it when he rescued her from the Bartoll. He succeeded in the OAV, but horribly failed in OG Gaiden, and later has to leave it to Axel to actually rescue her and restore her mind.
And also included in Magical Girl Lyrical Nanoha StrikerS, though it may be a bit unimportant, considering it came in the last episode of the last season. After Signum beats Zest and gives him a honorable death, Agito prompts Signum to watch over her and see if Signum can really follow up Zest's last wishes and his ideals. Signum's response? "If you ever see me straying from that direction, kill me." More proof that Signum is a magnificent Expy of Lamia.
Get Backers: Ban promised Yamato that he would protect Himiko from her curse, and Juubei promised to stop Kazuki if he ever strayed "from the path of righteousness."
Katekyo Hitman Reborn!: Squalo promised 8 years ago to Xanxus that he will never cut his hair until Xanxus becomes the boss of Vongola. And he did, for eighteen years into the alternate future from the Ten Years Bazooka. Obviously because Xanxus doesn't have the blood of Vongola, thus it's impossible for him to become Boss.
Blood+: Saya makes Haji promise to kill her after she defeats Diva, a promise which he is unable to keep, instead encouraging her to live.
Nabari No Ou: Miharu's promise to Yoite, made under duress, to erase Yoite's existence once Miharu can use the Sinrabanshou becomes the main tension and plotline of the series, as well as a source of a lot of its angst.
Madlax has Madlax and Vanessa promising each other to survive. It looks like Vanessa fails, but along comes Margaret ex machina...
And then one remembers that their souls fused and any lies on either side would've been known and that Yubel didn't know that Juudai had remembered their past together. Yubel had nothing to do with his memories reviving. That happened because he'd actually inflicted damage on Yubel, which almost no one can do, since Yubel's effect is to take no battle damage at all. Not to mention that if Yubel lied, it would've been a part of the plot. Juudai loves Yubel. Their past is not a lie.
Negi promises Ako that he will win the tournament. At about the ten second count, he recalls the promise and gets up to face Rakan once more. It's actually at tie and Rakan could have beaten him if he really wanted to. But considering the shape Negi was in? Badass.
Chrono Crusade has several promises that the main characters take very seriously. The first is that Mary Magdalene made Chrono promise to "live", which is implied to be the only reason he didn't commit suicide after her death. Also, the manga version shows Joshua and Rosette promise as children to "grow-up together"—remembering his promise is what gives Joshua the strength to reject Chrono's horns. Also, when Rosette made her contract with Chrono, Chrono seems to have promised himself that he would protect her, even going to the point of saying he promised to "never make her cry" in the manga. When he's forced to break this promise at one point, he becomes really pissed.
In Tiger & Bunny, Kotetsu made a promise to his wife on her deathbed to continue to be a Hero after she was gone. This promise starts getting harder and harder to keep once Kotetsu starts losing his powers.
Sosuke's father doesn't make it home as he promised.
Sosuke promised Ponyo to keep her safe, and she's swept away by the sea.
Sosuke's mother promises she will come back; Sosuke and Ponyo set out in search of her when she doesn't.
Code Geass has several. A couple of them are found on the Pinky Swear page and are explained in more detail there. A non-pinky promise comes during arguably the biggest Crowning Moment of Heartwarming in the series; when Lelouch realizes how much his friends care about him, he tearfully promises them that he'll set off fireworks with them again someday. He doesn't, and when he realises he won't be able to keep this promise, he calls them to apologize and say goodbye.
In One Piece, a band of pirates left a baby whale they adopted named Laboon at the beginning of the Grand Line, promising to return after they've made the round-world voyage. Unfortunately, those pirates were wiped out, half becoming ill and having to leave the ship to save the rest, and those that remained were wiped out in a battle. Of those pirates, only Brook remains, having been brought back to life as a skeleton by his Devil Fruit. And now he has promised to his dead crewmates to deliver the final message of the Rumbar Pirates to Laboon, even after fifty years.
During their childhood, Luffy and Ace made one promise to each other after the death of their third brother Sabo: they would live their lives free of regrets.
The steward promises to protect the young lord on his journeys, and promptly becomes The Oath Breaker.
"If I be not true to my master," he said, "Christ himselfe be not trew to mee! If I be not true to my lord and master, An ill death that I may die!"
The young lord saves his life by promising to never tell anyone about the steward's having attacked and robbed him. (He gets around this through Exact Words.)
The duke's daughter the steward was wooing pretending to be the young lord, on learning the truth, promises to marry no one but the true lord.
"If you doe not my councell keepe, That I haue told you with good intent, And if you doe it not well keepe, Ffarwell! my life is at an ende." "I wilbe true to thee, Lord of Learne, Or else Christ be not soe vnto me; And as I am a trew ladye, I'le neuer marry none but thee."
Usagi Yojimbo has the story A Promise In the Snow where the titular character promises a young girl her gravely wounded father won't die. After they're all nearly buried by an avalanche and Usagi has been battered unconscious, the girl invokes Usagi's promise to get him back on his feet.
In "Bearskin", the hero, appalling shaggy, filthy and ragged, but rich, rescues a man from financial distress, the man promises that he may marry one of his daughters. Only the youngest is willing. However, his appearance stemmed from a Deal with the Devil, and that being over, he cleans up nicely and formally arrives at their house as a wooer — or, in some variants, at his own wedding. The older sisters are impressed, but the youngest, being the sort who would marry a hideous man to redeem her father's promise, ignores him until he proves that handsome as he is, he is still the same man whom she promised to marry.
In "The Frog King", the king insists the princess must keep her promise to the frog who helped her.
In "Parsley", when the ogress catches the mother in her garden, she makes her promise to give up her child. When the girl is about seven, the ogress tells her, repeatedly, to remind her mother of the promise.
Every time she went along the street and met the ogress the old woman said to her, "Tell your mother to remember her promise." And she went on repeating this message so often that the poor mother, having no longer patience to listen to the refrain, said one day to Parsley, "If you meet the old woman as usual, and she reminds you of the hateful promise, answer her, 'Take it.'"
In "Rashin-Coatie", The prince knows that the henwife's daughter (who cut her foot to fit in the shoe) is not the woman he fell in love with, but is bound by his promise to marry the woman whose foot it fit.
In "The Pied Piper Of Hamelin", a piper saves a town from rats by playing a magic tune that makes the rats drown themselves. When the citizens of Hamelin deny the piper the payment formerly agreed on, the piper in retribution uses his music to lure the children of Hamelin into a cave which closes forever with them inside.
The legendary mermaid Melusine, is found near a woodland spring. She falls in love with the human who finds her, and agrees to marry him, on the condition that he not peek at her while she bathes. They are Happily Married for awhile, raising several children (all of whom are more like demons or demigods, depending on whom you ask), and settling into a nice chateau. Buut, one day, her hubby's curiosity and/or lust gets the better of him, and he peeks in on her bathtime, and finds out that she's actually a mermaid. (He sees her tail fin.) Melusine is not happy, to say the least.
Notably, her own father broke a similar promise made to her mother, Pressyne. She, however, was satisfied with taking her three daughters and walking out on him.
In Tattercoats, her grandfather had sworn an oath never to look on his granddaughter's face.
In The White Dove, two princes promise a Wicked Witch their brother if she will save them. Years later, after the brother had been born and grew up, the witch claims him.
Later, the witch must carry out her promise to let the prince have the kidnapped princess.
Sir, unless I have a wife as white and red as this cheese, it is all over with me; so now resolve, if you wish to see me alive and well, to give me all I require to go through the world in search of a beauty exactly like this cheese, or else I shall end my life and die by inches
In the Film Noir-esque fanfic Nights In the Big City, http://www.fanfiction.net/s/3560875/1/Nights_in_the_Big_City, Kim Possible makes a promise to Ron to sleep with him after he takes a flamethrower to the chest for her to motivate him to hang on during surgery. Afterwards he tells her that he knows why she made the promise and won't hold her to it. She does anyway.
The German film Das Versprechen literally means "The Promise." It's about a teenage couple in which the girl escapes from East Germany, and her boyfriend promises "Ich komme nach" (roughly: I will come after you). The movie's plot is basically how difficult that is for him to accomplish.
In Much Ado About Nothing, Beatrice asks Benedick to prove his love for her by killing Claudio. At first he refuses (saying, "Not for the wide world") because Claudio is his friend and companion. When she continually insists that he do this to avenge the wronging of Hero, Benedick eventually agrees. Benedick confronts Claudio, but everything is resolved before the duel can happen.
A plot point in Friedrich Dürrenmatt's eponymous Das Versprechen (The Pledge), where a Swiss Police Commissar promises a couple to track down the murderer of their young daughter. This promise subsequently drives him to madnesswhen he can't find him.
The poems of Robert Service occasionally feature these, such as "The Cremation of Sam McGee" or "The Ballad of Blasphemous Bill". In the former, a man must carry Sam's dead body around with in the Arctic him until he finds a place to cremate him, and in the latter, an undertaker has to journey out to find Bill's dead body and give him a proper burial. Except that his rigor mortis prevents him from fitting into the coffin. Why, look. A hacksaw.
As of Thud!, Sam Vimes reads the same book to his son at six o'clock, every day, no excuses (because when you have a good excuse, you open the door to bad excuses). As for the onemoment he can't make it in time...
In the Sword of Truth series, it's mentioned several times that "A Wizard always keeps his promises." At one point, a secondary character tells the main character that the reason this happens is, as a wizard, he's subconsciously using his magic to make sure the promise is kept.
In the novel The Oathbound Wizard by Christopher Stasheff the wizard Matt Mantrell makes a careless hyperbolic vow to overthrow a nearby Big Bad. Since he lives in a magical world with similar laws to Medieval legend, he is honor bound to do so. He later convinces God that the vow was made in error and he shouldn't be held to it, but by then he has seen how horrible the Big Bad is and wants to overthrow him anyway.
In George Mac Donald's The Princess and the Goblin, when Curdie helped her and the nurse get home safely despite the goblins, Princess Irene promised to kiss him. Leading to the complications in the page quote.
In Graham McNeill's Warhammer 40000Horus Heresy novel False Gods, Loken explains to Karkasy "the promise of moment" a promise to do one specific thing, and extracts from him a promise to keep their conversation secret.
In Robin McKinley's Beauty, Beauty is told not to go into the forest. When she thinks this means far in and goes in around the edges, her brother-in-law makes her promise not to. She dislikes giving her word on principle — then she has to keep it — and so insists that he give his word too.
In Neil Gaiman's Coraline, Coraline goes to pry a promise out the Other Mother, who first tries to swear on her mother's grave. When Coraline asks if her mother has a grave, the Other Mother says she put her there herself, and put her back when she crawled out. Coraline insists on something else, and the Other Mother swears by her strong right hand. When she breaks it, she sends her hand after Coraline.
"Do you think," she began again, after a minute's silence, and with a visible embarrassment of manner most unusual in her, "that a promise, deliberately and solemnly given, is always binding—except, of course, where its fulfillment would involve some actual sin?"
In The Silmarillion, Fëanor and his sons swore a terrible oath to recover the Silmarils at any cost. These Silmarils were three hallowed jewels which Fëanor made, and which Morgoth stole. Centuries later the oath destroyed them thoroughly, and resulted in them slaughtering many innocents. Even after the last two surviving sons thoroughly hated the oath and wished to stop killing people over the jewels, they felt (or thought they were) somehow compelled to continue.
In The Lord of the Rings, Aragorn can summon the Dead to fulfill the oath of assistance that they did not respect centuries before.
The Godfather: Don Vito Corleone basically operates by getting these from a great number of people. (The novel says that he piled up good deeds like a banker piles up securities.) Interestingly, we never see him extort any criminal acts from the recipients of his "favors"; instead, he gets completely innocuous freebies from whatever their normal business is. (Wedding cakes from the baker, performances at his casino from the singer, and a funeral from the undertaker when Sonny gets whacked.)
In Robert E Howard's "The Vale Of Lost Women" Livia promises herself to Conan the Barbarian if he will free her from her captor. Then she bolts in panic. When he rescues her again, she admits to breaking it and deserving punishment; he returns her home instead because it would have been no better than rape.
A shudder shook Kull's gigantic frame. "Valka! But what a fate! Hark ye"—his fingers closed upon Brule's sinewy arm like steel—"hark ye! If I am wounded unto death by these foul monsters, swear that ye will smite your sword through my breast lest my soul be enslaved." "I swear," answered Brule, his fierce eyes lighting. "And do ye the same by me, Kull." Their strong right hands met in a silent sealing of their bloody bargain.
In Robert E Howard's Kull / Bran Mak Morn story "Kings of the Night", Bran's problem is that one tribe is willing to break its promise if it does not follow a man of its own blood.
In L. Jagi Lamplighter's Prospero's Daughter trilogy — too many to shake a stick at. From the promise of the aerial spirits to obey the Prosperos, to Theo's promise to himself to give up magic, to Logstilla's promise not to become attached to her children any more, to Miranda's to Mephisto's familiar not to reveal their conversation to Mephisto. And many more!
In Juliet Marillier's Son Of The Shadows, the heroine refuses to give her promise to stay in Sevenwaters to the Fair Folk, knowing that it will come back to haunt her if she does - The Fair Folk always get what is promised to them.
In Between the Rivers by Harry Turtledove, the protagonist in a grandstanding moment vows that he won't marry his sweetheart until the completion of the trading expedition he's about to embark on. It seems like a safe thing to do since it's a routine expedition and he wasn't planning to marry her until after he got back anyway. But then the nation they were going to trade with unexpectedly puts a trading embargo on the protagonist's city. And the god he swore by is real, interventionist, and quite willing to make the vow stick.
The Warrior Cats novel Crookedstar's Promise. A mysterious spirit cat asks the main character, as a kit, to promise to be loyal to his Clan above all else, even his own desires. Naturally, he promises, since he can't imagine not being loyal. Turns out that she meant that he can't take a mate or anything of the sort, and she definitely didn't have his or the Clan's best intentions at heart.
In Edgar Rice Burroughs's The Monster Men, Professor Maxon promises that von Horn can marry Virginia if he rescues her, in the heat of the moment. Afterward, he realizes that this was a problem since he had not gotten Virginia's consent.
In John C. Wright's Count To A Trillion, Menelaus's mother explained her cruel punishment on the grounds that Darwin required it. The young Menelaus concluded that Darwin was a villain, and promised that he would stop him.
In George Mac Donald's "Port In A Storm", the narrator got his uncle to not interfere with his wooing the uncle's wealthy niece, despite the appearance of trying to get at her money, by bringing him port to drink during a storm and collecting this as his reward.
In Seanan Mc Guire's Velveteen Vs, Velma, warned by Scaredy Cat, demands a promise that she can go home before she hands over the pumpkins.
Live Action TV
Torchwood: "Tommy, you're my big handsome hero, and I need you." (Interesting Western example with English and Japanese characters as the promiser/-ee.)
John promises to give Scorpius all of the wormhole knowledge in exchange for help rescuing Aeryn. This debt is later wiped out when John comes up with a way of hurting the Scarrans, which makes Scorpius VERY happy.
John promises to Aeryn that he wouldn't hurt Scorpius, since Scorpy saved her life. Aeryn releases him from the promise. They never intended to kill him, anyway.
Sam Tyler promised Annie he wouldn't leave her at the end of the finale, and mentioned that promise to his mum afterwards. And he kept his promise.
Several promises have been made on Merlin. Freya promises that one day she will repay Merlin for his help, and does so by delivering Excalibur into his keeping. Arthur promises Guinevere that when he is King, they'll be together. Whilst held hostage by a warlord, Lancelot promises Guinevere that he'll rescue her - this thus far is the only promise that hasn't been kept - whilst Lancelot does his best, it is Arthur and not Lancelot that rescues them.
In Planescape: Torment, your character can actually do this as a dialogue option. Sometimes, dialogue choices (in some specific, important and dramatic scenes) will have a declaration of intent hidden, such as "Truth", "Lie", and, most importantly, "Make Vow". Those dialogue choices affect your Character Alignment: you become more Lawful if you tell the truth, and more Chaotic if you lie.
A promise is the driving force behind the plot of Disgaea 4, hence the title. The main character, Valvatorez made a promise to give his Prinny trainees a sardine once they finish their training. However, the Netherworld's government decides that all of the Prinnies need to be exterminated to cut back on expenses, which would keep him from fulfilling his promise. So naturally, he decides to overthrow the government.
Kingdom Hearts: At the end of the first game Sora makes a promise with Kairi that he'll return to her and the island with Riku someday.
In a deliberate echo in Kingdom Hearts II, Roxas makes a promise that he'll meet up again with his friends in Twilight Town. Sora fulfills it vicariously for him, and gets the Oathkeeper keyblade for doing so.
In Castlevania: Aria of Sorrow, Soma Cruz asks Julius Belmont to promise to kill him if he turns evil. Thankfully, the person making the promise is reliable and more than strong enough to fulfil said promise if it comes to that. In Aria's bad ending, Julius turns up in the throne room to kill Soma, and in Julius Mode in Dawn, Julius gets Yoko and Alucard's help to take down Soma.
Soma: ... I've got a favour to ask of you.
Julius: What is it?
Soma: From here. I will set off to fight against my own fate. If I lose the battle... And I become reincarnation of evil, I want you to kill me.
Julius: ... I will... I promise.
Soma: Thanks. Now I can go into this battle without reservations.
Julius: Farewell, my friend. Don't let me use that whip again.
If Shepard enters into a romantic relationship with Liara in Mass Effect, at the conclusion of Lair of the Shadow Broker in Mass Effect 2, Liara asks Shepard to promise her that s/he's always coming back. He does. Both she and Tali beg you to come back after the final battle in Mass Effect 3. Since it's currently assumed that ME3 is the end of the series (for Shepard), in one out of three endings, with a high enough EMS score, you can assume he keeps his promise. Who knows what'll happen now that Bioware has broadly hinted that Mass Effect 4 might be worth keeping your saves for though.
The Order of the Stick: Roy's father, Eugene, swore a Blood Oath of Vengeance to seek out and destroy Xykon, the Big Bad. His failure to do so, plus his decision to abandon his quest, keep him in limbo even after his natural death and transfers the obligation to his heirs.
He's incensed when his son, Roy, gets to go on to the afterlife proper, since Roy didn't fulfill the terms of the Oath either. It's pointed out by a Being of Pure Law and Good that Roy gets to move on because he died in direct pursuit of the quest his worthless flake of a father dumped on him by consciously abandoning it.
Adventure Time: Princess Bubblegum makes Finn "royal promise" not to tell anyone about the zombies. He has a hard time keeping it, but eventually he defeats the zombies without telling anyone. When Jake discovers the hacked bodies around him, Finn feels it's alright to tell him. Only it's not: turns out the consequences of breaking a royal promise are having to face trial by fire at the hands of giant gumball dispensers. Luckily, it gets negotiated down to 'trial by math.'
Up: As kids, Ellie makes Carl promise to help her get to Paradise Falls. She never gets there, but Carl's desire to fulfill his obligation drives the plot of the movie. Later, Russell has Carl promise to keep the bird he befriended safe, and Carl's conflict between the two promises drives the second act.
Rapunzel from Tangled takes promises very seriously and says that she never breaks them. This comes into play later when she promises Mother Gothel that she will be her prisoner forever if she lets her heal the fatally injured Flynn.
In the after-series comic in Avatar The Last AirbenderZuko makes Aang promise him to kill him if Zuko starts to turn into his father.
In Titan A.E., during the evacuation of Earth, Cale's father puts him into the care of an alien friend, and promises his son that he'll see him again. He doesn't, but leaves a message for Cale begging his forgiveness for breaking his promise.