The Child of Love: In the sequel Takuma Satori, a boy who met and befriended the first Rei for a short while when they were little kids, shows up. Takuma had a crush on Rei, but whether he was unlucky or victorious is not known due to the sequel being unfinished.
Child of the Storm has Loki and Sif, who seem to be blind to how into each other they are (particularly the guilt-riddden Loki), while Everyone Can See It and pretty much everyone (particularly Fanral for some reason) is a Shipper on Deck). It gets to the point where part of Harry's plot critical letter from the future is an irritable exhortation to his uncle to open his damn eyes. As of the time of writing, there's no sign if it will be victorious or not, but it seems to be getting that way. As of Chapter 77, they finally get together, with a bit of help from the Warriors Three.
Harry and Carol spend most of their time dancing around this, insisting that they're Just Friends... in the middle of flirting each other's metaphorical pants off. Even supervillains have started noticing it. They finally hook up in chapter 46 of the sequel.
Ghosts of Evangelion: Kyoko reveals that Shinji and Asuka met for first time when they were little kids. Subverted because neither of them remembered it:
Kyoko: We went to college together, as I understand it. She and I spent a bit of time together after you and Asuka were born, before Asuka and I left for Germany. Asuka:[laughing] So we'd met before? Me and the idiot, I mean. Kyoko: I actually remember that, too. I remember staring down at you, thinking you were the cutest thing ever, while Yui did the same with Shinji. Asuka: How about that, eh? The red string of fate bound us together even then. Kind of depressing, now that I think about it. Shinji:[laughter]
Once More with Feeling: A NERV officer reveals Shinji that he and Asuka had met for first time when they were toddlers... and they already fought back then. Shinji finds it both amusingly ironic and disturbing. Asuka finds it hilarious.
Used in A Pleasant Surprise, when it is revealed at the end that Fluttershy and Midnight have known each other since childhood.
Blind gives us Naruto and Hinata. These two have known each other their whole lives and marry. Justified in that they spent every living moment (potty breaks and a baths excluded) together, due to Hinata being blind, from birth and continually hold hands.
It's common to portray canon married couple Shining Armor and Princess Cadence as having known each other since they were both foals, due to their connections to Twilight Sparkle. It's also very common for Fluttershy andRainbow Dash, who are childhood friends, such as in How We Met.
Many writers also like to portray Princess Celesta and Discord as having a past together before Discord attempted to take over Equestria. Following his reform, the writers like to think they're giving their relationship another try.
Following the season five finale and season six premiere, fans have started writing stories involving reformed villain Starlight Glimmer falling in love with her childhood friend Sunburst.
In The Flash Sentry Chronicles, Flash Sentry and Twilight Sparkle have been best friends ever since childhood, with Twilight's family taking him in after he helps her and they learn he has no family himself. Their friendship slowly evolves into something more, even if it takes them both a long time to realize it.
Hivefled: The Grand Highblood and the Condesce (who met when the Condesce was a preteen and the GHB was a baby). As moirails who are sexually involved, they're violating the taboos of troll culture, and then there's their endearing little hobby of bonding via the sexual abuse and murder of teenagers. One of the character bios for the story specifically notes that trolls (who aren't raised by their biological relatives) have no Westermark Effect.
In The Matrix and Supernatural fanfic Hunting Series Neo and Dean met after John saved Neo/Tom Anderson from vampires as a kid. During highschool Dean attended Tom's school for a few months. Years later, when Neo goes from being a rebel/the One to a hunter they eventually go from just friends to lovers.
Chiyo Ueda of Despair's Last Resort reveals that she was in love with a friend she knew since they were kids. Unfortunately she never knew how he felt before he died from a terminal illness. Kumiko Akamine also seems to have had this with Gundham Tanaka.
A good number of Death Note fanworks have Matt and Mello falling in love at Wammy's House. Often (though not always), they reunite after a period of painful separation after Mello's In-Universe decision to leave Wammy's upon being told he'd be expected to work with Near.
In Son of the Seven Kingdoms, William and Arya become the best of friends during his time fostering at Winterfell. When their fathers set up an Arranged Marriage between the two of them, it's intensely awkward at first, but as time goes on their feelings for each other bloom into an intense and genuine love.
Cells at Work! fanfics that pair AE 3803 and U-1146 together like taking their first meeting as kids and turning it into a full-blooded childhood friendship. The fact that she never recognised him as the same kid is usually retconned away as her memory problems causing her to forget everything after the Bone Marrow incident.
In You Built This House, Darling and Apple met as kids. It was a mutual attraction even then. Years later they meet again as teens. It turns out that they're destined to be together, though Apple is very deep in denial about her attraction to girls for most of the fic.
The animation Strangers depicts Sweetie Belle and Button Mash as childhood friends who grew apart. They still miss each other.
A onesided variant appears in Married to the Koopa King. Bowser has fond memories of being Peach's childhood friend, but Peach quickly outgrew their friendship. The fic routinely teases that Peach could requite Bowser's Villainous Crush in the future.
25m Distance Between Us presents Pauline and Mario as being childhood friends turned high school sweethearts. They had a good relationship (a few arguments aside) until Mario became a plumber and mysteriously disappeared one day.
Sunsplit Saga: The potential romance between Starlight Glimmer and Sunburst, who knew each other as children, as specified in the source material, and that the latter had a crush on the former, as indicated in the first story. The third story indicates that there is likely reciprocation, given how Starlight's "face went from merely arguably pink to definitely pink", when Sunset Shimmer asked her, "So, again, why aren't you tongue tangoing the tasty treat that is your childhood friend?"
Subverted in the oneshot So the Trauma. Everyone (including Kim herself) thought Kim and Ron, her best friend since pre-K, were destined to be together. That is until Kim realizesshe's gay.
Mirrors (TLOZ): Sheik explicitly states that Link was his childhood friend and childhood crush. Though he worries that Link only likes "Zelda", it works out between them.
Naruto and Hinata met under more or less identical circumstances to canon in Son of the Sannin, though Shizune's intervention means that they become close friends in their early childhood instead of Hinata simply pining for him from afar for over a decade. Pretty much everyone is aware of their feelings for each other and they start dating in chapter 31 after they're both promoted to Chunnin.
In the Ranma ½ fanfic Same Time Next Year, Ranma and Akane meet shortly after Ranma learned the Neko-Ken and develop a friendship which slowly turns into love.
Sayaka and Kyoko in Advice and Trust have been best friends their entire lives and were engaged in a Secret Relationship at the time the series began (which later develops in to a polyamorous relationship with Kensuke). Sayaka actually mentions at one point that they've been in love with each other since before they were old enough to talk.
Kanto Calling: Misty's seventeen and has had a crush on her friend Ash since they were ten. Ash also likes Misty as well, but neither he nor Misty will admit to it.