Many years ago, Alice and Bob met each other by random chance, and the meeting left a deep impression on at least one of them. But years have passed, and now they're grown up (or at least in High School). All unknowing, they have been pulled back together by the Red String of Fate - friendship, romance and/or adventure will see them rekindle a long-lost connection long before they realize that they've met before. The realization that their new friend is the same kid they met years ago may come slowly with heavy foreshadowing, or be a sudden twist.
A classic setup for the romantic anime, when the Childhood Marriage Promise would be a bit too blatant. Quite popular in western shows as well, however.
Related to Already Met Everyone and Childhood Friends. Contrast Forgotten Friend, New Foe, Old Flame Fizzle.
Anime and Manga
Nogizaka Haruka no Himitsu: It eventually turns out that Yuuto was the one who got Haruka into anime and manga in the first place when, as a kid, he found her crying in a playground on his way home from a shopping-trip with an Otaku friend, and gave her a manga magazine. The incident didn't leave a huge impression on him, but it essentially changed her life - arguably for the better. (Though her Overprotective Dad might disagree...)
In Ai Yori Aoshi there's a broken Childhood Marriage Promise but she wants to find him. When she does he doesn't remember her at first. There are flashbacks, not to the first time they met but while the were friends as kids together.
Panzer World Galient: When Jordy and Asbeth arrive at White Valley, Jordy meets and befriends White Valley's leader's girl, Chururu. Shortly after Asbeth and Chururu's father explain to both they had already met when they were two-years-old, during an ealier visit of Jordy's "grandfather". Naturally, since Jordy and Chururu were toddlers back then, they had completely forgotten that.
Pokémon: Barry doesn't remember that he and Dawn met when they were younger. Granted, they're probably only ten or eleven...
Ash and Serena met in a summer camp held a few years before Ash started his journey. Ash remembers the event, but not Serena specifically (a bit justified since that was likely the only time they met).
Pokémon Special: Ruby and Sapphire meeting each other as little kids led to Ruby to becoming more delicate and feminine, and Sapphire wilder and tomboyish. When they met in series they both couldn't stand the other's new persona, nor did they remember meeting each other before.
In Mamoru-kun ni Megami no Shukufuku wo!, it gradually becomes clear that the Beatrice-user who saved Mamoru during a disaster when he was small, was Ayako's uncle - and what's more, she was there too. Neither one of them remembers at first due to having been quite young and traumatized to boot, but that event was the reason why Mamoru decided to become a Beatrice-user himself, which led to him joining the Beatrice Academy, where he, of course, met Ayako again...
Love Hina is probably the poster child for this trope. Keitaro knows about his childhood friend whom he promised to get into Tokyo University with... he just can't remember her name or face. It turns out he had two childhood friends: Naru and Mutsumi.
Fruits Basket's Tohru met Yuki when they were younger, but it isn't until later on in the series he realises she was the same girl. He believes she doesn't remember but actually the memory was very important to her, even though she never learns that Yuki was the boy.
In Hyakujitsu No Bara, Klaus and Taki meet briefly in the middle of a forest by chance when they are young and make something of a Promise. Years later, they meet again and Klaus recalls but continually dismisses the memory, until their Relationship Upgrade, when he realizes from Taki's scent that it was him.
In Tokyo Babylon, Subaru meets Seishirou as he cradles his kill, and they end up making a promise. Years later Subaru only remembers this as a vague dream, and has little idea why Seisshirou has suddenly appeared in his life as a suitor. Unfortunately the memory isn't a very happy one, once it's revealed.
In the Saint Beast drama cds, Rey reveals to Shin that he had met Luca long before the day he actually introduced himself, and felt guilty for hiding it. In their adolesence Luca found Rey crying and lost in a forest and led him out. After searching out his rescuer, Rey was too embarassed to introduce himself until many years later when he received wings and felt he had something to bond over. Shin remarks that Luca probably knew all along and was too gracious to say anything.
In Junjou Romantica, Nowaki recalls the day he found out the orphanage owners weren't his real parents and tried running away. He stops at a park when his tires go flat, only to have his future lover walk by, inquire, and then start dishing out life lessons about the obstacles kids must get through before tattling to the patrolman. Years later Nowaki remembers the encounter and mentions it to Hiroki, but neither realizes it was each other.
In the original OAV animated version of Ah! My Goddess, Keiichi and Belldandy met when they were children. After Belldandy made a promise with him, it was considered as she made a contract when she didn't have her qualification yet. She had to erase Keiichi's memories of her and promised to return to him once she gained her qualification.
Kenichi: The Mightiest Disciple: When Kenichi was a kid, he and Ryuto met Miu. After seeing Miu defeat the thug trying to assault a kind old lady, both Ryuto and Kenichi vowed to become strong, but Kenichi forgot the fact. Miu apparently recognized him right away, but didn't feel the need to bring it up when they meet again.
In Axis Powers Hetalia, Germany is hinted to be Holy Roman Empire, Italy's Love Interest when they were little. It's not clear whether Italy believes them to be the same person or not, but Germany, at least, appears to have forgotten about their shared childhood. He might have remembered in the Valentine's Day strip, but that plotline has been abandoned for years now.
The first Sailor Moon movie explained how Usagi and Mamoru first met. A 10-year-old Mamoru was in the hospital after being in a car crash that his parents died in. Fiore is an alien disguised as a human who was ill because he couldn't survive on Earth at the time (though he adapts). 4-year-old Usagi is there to visit her mother who is giving birth to her younger brother Shingo, and she sneaks into Mamoru's room. Usagi and Mamoru talk for a bit, then Usagi gives Mamoru one of the roses she had originally brought to give to Ikuko-mama. Mamoru then gives that same rose to Fiore as he leaves Earth.
In Skip Beat!, Ren and Kyouko actually met when they were young children, not when they were first introduce at the agency. Ren is actually Kyouko's long-lost childhood friend 'Corn,' which just makes it even more ironic that she starts the series off hating him. Ren knows, but Kyouko is still in the dark about their pasts.
In Popcorn Avatar, Kurando has met Lisa before, way back when he was still in 3rd grade, when she was crying in the park after being bullied for her beautiful blonde hair. He remembers this again after a short bout of memory regression however.
In Revolutionary Girl Utena, it's revealed near the end that Utena had met Anthy before when she was just a kid, and that her desire to save her from the million swords of hate is the true reason why she desired to become a prince.
In Kara no Kyoukai, Mikiya Kokutou first met Shiki Ryougi as he was walking home in the snow and paused to talk to her, but when they met later once they started at the same high school she didn't recognize him. At the very end of the series we find out why, since Kokutou was actually talking to Shiki's third personality, who was unknown even to her at that point in time.
Played for painful drama with Kouichi Sakakibara and Izumi Akazawa in Another. Though they only met a few years prior to the story, the forgetfulness is justified since Kouichi was only in Yomiyama for the funeral of his aunt, a time erased from everyone's memories due to the events of the curse. Akazawa remembers seconds before her death. Kouichi doesn't.
In Nine Rules to Break When Romancing a Rake, the couple met when she was barely out of her teens, he was older; he was kind to her, she was smitten. Many years later, she decides to pursue him. When she's won him, she tells of their early encounter — he doesn't remember it at all, and laments that if he'd only recognized her true worth at that time, they wouldn't have wasted so many years apart.
Subverted in Saki. Hisa played against Mihoko once in middle school, and Mihoko was so surprised that she opened her right eye in surprise. As the game ended, Hisa told Mihoko that she found her right eye pretty. Hisa never showed up for the tournament the following day, went to a different high school from Mihoko, and when they faced each other again, Hisa was unable to recognize Mihoko. However, during the individuals, when Mihoko faces Hisa again and opens her Magical Eye, Hisa remembers the meeting, and afterward, the two become quite close.
In Nisekoi, Raku met every single girl in his Unwanted Harem when he was a kid, but it takes a while for him to even find out about it. At first, most of them don't know about it either. The problem is that there are three girls who remember having made a Childhood Marriage Promise with him, but he only remembers to have made the promise to just one girl.
In Part 4 of Jojos Bizarre Adventure, it turns out that Reimi, the ghost girl who kicks off the hunt for Serial Killer Kira, once babysat for Rohan, and ended up throwing him out of the window of her house to save him from Kira the night she was murdered. The event was so traumatic that he eventually used his stand to erase the memory from his mind.
Nozaki's first meeting with Sakura in Gekkan Shoujo Nozaki-kun actually inspired Mamiko's physical appearance (and made Sakura fall for him), but he doesn't remember this because he was so exhausted that day that his memories of it are fuzzy.
In The Phantom the hero and his love interest meet for the first time in the first story arc, until Lee Falk wrote the story of "The Childhood of the Phantom" and included a scene where they met briefly years before when they were both children.
When Mary Jane Watson revealed to Peter Parker that she knew he is Spider-Man, she also told him quite a bit of her life story, including that she had seen him raking leaves through the window of her aunt's house (May Parker and Anna Watson were neighbors) and thought he was cute even before he became Spider-Man.
A few Superman stories over the decades depict Clark Kent and Lois Lane meeting as young teens, sometimes with Clark becoming Superboy. A few stories also have young Clark meet young Bruce Wayne.
Once More with Feeling: In chapter 9 a technician told him Shinji that Asuka and he had already met when they were toddlers (something both of them had utterly forgotten about). Asuka's mother was visiting the Japanese Branch and left both in a play pen, and they... well, they fought. Shinji got a good laugh of it (thinking that some things never change), and so Asuka did when he retold her the episode to her.
In The Princess and the Frog, Tiana and Naveen meet minutes after he arrives in New Orleans. He tries to woo her, but she ignores him and he moves on, even saying "Eh..". He fails to recognize her when they meet again at the party, though.
In Spirited Away, Mysterious Protector Haku knew Chihiro's name even though he couldn't remember his. Chihiro kept having a feeling that she met Haku from before but couldn't remember when. It was only when they were flying through the air together that Chihiro remembered she fell into a river as a little girl, only to be saved by the spirit residing there. Chihiro recalling this memory to Haku caused him to remember his identity.
In Anastasia, Dimitri used to work as a servant in the Winter Palace when he was a boy, and he was the one who saved an eight-year-old Anastasia/Anya from being captured in the Revolution.
Brian Allen and Christina Roberts in Blow Dry. They knew each other as very young children because their fathers were business partners. But then the partnership broke up, Christina's parents divorced (and she went to live with her mother in Michigan), Brian's parents divorced and he moved in with his dad in York, and the two lost touch with each other for twenty years. Cue the events of the film...
The prologue to the movie Adam and Steve features the two main characters hooking up in the 80s and having spectacularly bad drugged-out sex. They meet, sober and professional, 20 years later and don't realize it's the same guys till almost the end of the film.
Two of these occurred in A New Hope due to new information revealed in the prequel movies. First of all, C3PO didn't know who Obi-Wan Kenobi was, but R2D2 did, and he didn't remember them, although he clearly knew them both when he was younger, making his interactions with them in the prequels somewhat confusing. This was partially explained at the end of Revenge of the Sith, where Captain Antilles orders C3PO's memory wiped, which erases his memories of the entire prequel trilogy. (It doesn't explain how Obi-Wan forgot, however.)
Who says Obi-Wan forgot? It's possible he did recognize them and just didn't say anything. This would be consistent with his characterization in the first trilogy because A). He's an old Jedi master familiar with the mysterious ways of the Force, and B). he was trying to shield Luke from the dark secret about his father.
Also, Luke's aunt and uncle didn't seem to remember C3PO either, although he had worked for their family for years in the time between The Phantom Menace and The Clone Wars. Owen may not have been telling Luke the truth about that, however, much like he was lying to Luke about the fate of his father in order to keep him sheltered. (The hologram of Leia probably made him decide against mentioning that he knew where the droids had come from.) Of course, it's just as likely that they simply didn't recognize C3PO; it had been over 20 years and the Protocol droid didn't have his iconic gold finish when he left their service.
In King Kelson's Bride, Kelson is reminded (by Rothana) that he had not only met his cousin Araxie when they were children, he also played with her and they got along very well with each other. Though their marriage is arranged, Kelson and Araxie decide to use those happy memories to build upon when forging their relationship.
Live Action Television
In Fringe Peter met Olivia as a kid, but seems to have amnesia about this ever happening even though he is Olivia's boyfriend now.
They both forgot this meeting as a result of repressing traumatic memories from around this time: for Peter, being kidnapped by his parents from an alternate universe; for Olivia, being the subject of Mad Science experiments.
In Community Jeff and Shirley realize that when they were children Shirley humiliated him in a game of foosball. Jeff moved away soon after and they did not meet again until they were adults. The humiliation turned Jeff into the Jerk with a Heart of Gold he is today and Shirley's Heel Realization made her a very passive person.
The Odd Couple: In one of the several versions of how Felix & Oscar first met, it was when Oscar's father ran a speakeasy in 1920s Chicago and Felix's father was an optometrist who fitted Oscar's father with glasses.
My Name Is Earl: Randy goes to meet his childhood crush "Pinky," who it turns out was Earl's ex-wife Joy.
Also, Joy originally tricked Earl into marrying her, given that her parents kicked her out for being pregnant out of wedlock. At the end of the series, it's revealed that the baby's father, whom she had a one-night stand with at a Halloween party, was Earl. Both were in costume.
In one episode Drake & Josh discover that they met when they were nine (rather than in high school as they previously thought).
In Iljimae, one of his love interests figures out who he was by a piece of jewelry the boy who saved her life carried. The other love interest also figures out who he was because he continued a story he never finished when they were children.
Dharma and Greg first saw each other as children when they barely missed meeting each other on a subway. Twenty years later they met on the same subway and fell in love.
An episode of Mad About You reveals that Paul and Jamie first met as kids at the Natural History Museum.
In Friends Ross finds out that Phoebe robbed him when they were kids.
Flashbacks also reveal that Rachel meets Chandler no less than three times: first as Ross's dorky roomate at Thanksgiving, then the next year as the guy Monica hated and then as Monica's friend in the bar. She remembers nothing when they meet in the Pilot though this is attributed to her teenage It's All About Me attitude.
The Vampire Diaries: Damon & Elena actually met the night of her parents death and not in the scene we see in 1.02.
In the Alien Nation novel Day of Descent, a flashback story about the spaceship crash five years before the series, Matt and George had a brief meeting in the climax of the book. But they didn't speak, and neither of them was able to tell members of the other species apart at that point, so they remain unaware that they've met before.
Doctor Who: Rose actually met the Doctor for the first time in the last moments of his tenth regeneration, months before she would meet Nine. Since he stayed in the shadows and they only spoke briefly, she doesn't recognize his face when he regenerates into Ten.
In the American Dear John, Ralph has a bad day and needs cheering up. John and Kate get him to remember something happy from his youth. He recalls a camper he used to have and enjoyed very much, but his happiness disappears when he remembers that a bunch of drunks stole it and rolled it into a gully. At the end of the episode, Kirk comes by and talks about his past. He mentions the time he and his friends got drunk and happened upon a camper.
A sequence in Final Fantasy VIII shows that either all or virtually all of the party members spent time in the same orphanage as children, and most of them don't remembered it - much less the fact that the person running said orphanage was Sorceress Edea, whose husband is Cid, headmaster of their mercenary training school. Irvine is the only one who remembers it all, due to not having used Guardian Forces until he joins the party - as it turns out, they can cause memory-loss with sustained use.
In Fire Emblem Tellius, Ike and Soren had met years ago, and Ike did not remember the first time that he met Soren, although Soren remembered in vivid detail. It was not until near the end of Path of Radiance that Soren bothered to remind Ike how they met, and it wasn't until Radiant Dawn that Ike finally remembered it first-hand. Justified in that their first meeting was right before Ike saw Greil killing Elena, for which Sephiran gave him amnesia which wasn't cured until being in the tower, where Ike and Sephiran's memories come to the fore.
Played with in Mass Effect. In the first game, you can encounter and destroy a rogue VI on Luna that has apparently gained sentience. In Mass Effect 3, you find out the VI was actually in fact EDI, the Normandy SR2's on-board AI and your eventual squadmate, in the early stages of her development. She remembered Shepard, but didn't want to say anything in case it made things difficult between them. Thankfully, she doesn't hold a grudge about it.
Deconstructed in To the Moon: The beta blockers Johnny takes after Joey dies leads him to suppress a large part of his childhood memories, causing him to forget why he wants to go to the moon and the first time he met River, this causes a great deal of resentment in River towards Johnny. As a result she futilely spent most of her life desperately trying to make him remember.
In Third Super Robot Wars Z: Jigoku-hen, Heero relates that back before he was a proper assassin, he had a mission here to guard the Tiger of Helmajistan. Who was evidently the charismatic leader of a guerilla force some ten years ago. His name was Majid, the Tiger of Badakhshan. Setsuna's familiar with him too, since he was sent here once before to assassinate him. Prince Ali apparently didn't like the guy, and sent Setsuna and some other kids to assassinate him. Sousuke chimes him that he also was here to get rid of him. Hibiki is shocked at the odds that three separate child soldiers might end up in the same region as enemies.
Harvest Moon series, Back to Nature and Friends of Mineral Town, the protagonist meets a girl as a kid, who turns out to be whoever you marries in-game via The Reveal.
This trope plays a large role in the 18+ Otome GameUnder The Moon, in which it is paired with Laser-Guided Amnesia and Played for Drama. Prior to the game, possible love interests Leni and Seizh were exiled for competing over the affections of the heroine Ashe, but she has forgotten them (through no fault of her own). Unsurprisingly, the guys are bitter about it.
In Kanon, it turns out Yuuichi knows all of the main girls except Shiori from childhood.
In CLANNAD, Kotomi and Tomoya met years ago when they were just children. She remembers, as Tomoya was her Only Friend, but he doesn't until right at the very end.
In Tsukihime, due to some Laser-Guided Amnesia, Shiki forgets about Kohaku and Hisui, and in the routes he does remember them, he cannot recall their names and also gets them confused due to the Twin Switch they accidentally pulled. Kohaku is not pleased, because she misunderstands and believes that Shiki thinks Hisui gave him her ribbon. Naturally, this means plan 'everyone has to die' commences as usual.
A plot point of the eroge Snow Sakura, the protagonist Yuuji once meets a girl under a cherry blossom tree. Since he's forced to move to the place of childhood, he determines to find out who the girl is. There are two possibilities for the girl's identity: one is Misaki, his class mate, and another is Saki, his cousin.
Too Much Information: The latest addition to Ace's Unwanted Harem is a very tall Ainu girl who ran away from home because she was always being mocked for her size, determined to find the only boy who'd ever called her pretty - a young Gaijin boy she'd found lost back in Hokkaido, and helped to find a police-box. Cue the revelation that Ace had gotten lost during a trip to Hokkaido with his mom when he was a kid, and had been helped by a pretty redhead...
Kevin & Kell does this with Rudy and Fiona, who find out after dating for some time that they were in the same preschool - and hated each other.
The Simpsons: Marge & Homer met when they were circa 10 years old at summer camp and shared their first kisses together. When they met again in high school neither recognized the other (in part because one had very different hair and the other had an eye-patch when they first met).
An episode of the 2003 Teenage Mutant Ninja Turtles revealed that the turtles had met Casey Jones when they were all kids, trying to teach him how to be strong. The turtles had disguised themselves, taking turns as to who would help him out, and Casey was using a different name (Arnold), so they never realized they'd met before.