Dungeon Keeper Ami features the Unraveller of Mysteries, one of a pantheon of dark gods hostile to Ami (So far she has encountered the god of martial force, the god of undeath/necromancy, the god of vermin; the Unraveller seems to be the dark god of mad scientists). It should come as no surprise that the Unraveller has such a huge following: the author has admitted that she was written with the voice of GLaDOS in mind.
Someone even wrote an epic ballad for him. Not bad for a random squid who shows up out of nowhere and immediately gets killed off.
Friendship is Witchcraft gives us Sweetie Bot, who has become one of the most recognizable characters and even has her own Tumblr.
Yawning Squirtle and Boulder-Dropping Whale in Sonichu, and Mary Lee Walsh, who is frequently the protagonist in various fanworks, and is drawn deliberately with a different design. This is mainly because many find that her real-life basis is actually pretty awesome. Plus, it ticks CWC off.
Bill the Scientist also qualifies for this, since he's also one of the Moon Pals.
Brother-Captain Allen of Tiberium Wars - stoic, calm, quiet, efficient, scary, and perfectly willing to mutilate rapists and then hurl them out windows. Its no surprise that such a bit character has become so liked.
Harry Potter and the Guardian's Light gives us THE INDOMITABLE ARGUS FILCH. In the novels, he's a slightly scary background character. In the movies, he ranges from creepy to disgusting or comic relief. But in this fanfic, his first scene involves him arming himself alongside Hellboy and John Constantine to go into the black forest and fight an army of trolls. Turns out, while he's not a janitor he turns a profit selling enchanted weapons. After he helps demolish the trolls with ease, we next see him tracking Harry down in his invisibility cloak despite not knowing it's Harry, or that he's in an invisibility cloak. Recently, Voldemort invaded the castle with an army of trolls and Filch was first on scene. His response was to ask them for a hall pass. He then ducked around a corner and they traded some fire. He was ordered BY VOLDEMORT to surrender. His response to that was to blow a troll's brains out, and say; "Alright, I surrender, now come a little closer!"It's easy to see why Dumbledore trusts this man to clean his school's floors.
Dragon Ball Z Abridged has Nappa. In the actual series he was a bland Giant Mook that was killed relatively expediently, but in Abridged he is quite possibly the funniest character in the series, and the fans loved him for it, to the point where he got to reappear several times as a ghost.
There is also popularity upon Super Kami Guru, Nail, Dodoria, Zarbon and The Ginyu Force (Specifically Recoome - these guys even got their own opening between Episodes 19 and 23.).
Warriors The Abridged Series (the abridged series of Warrior Cats, not something else), the most popular characters are Bluestar, Redtail, Matthias and Rainstorm. Redtail and Matthias each only appear in one scene. Well, there is Ghost Redtail, but then again, Redtail gained his popularity before that segment. And Ghost Redtail leaves when he realizes Tigerclaw doesn't like him.
While she was included mainly to intentionally avert the Ron the Death Eater treatment the character often gets, Ember in The Legend of Spyro: A New Dawn has been very well received by readers for being a kindhearted, friendly version of the character. This is part of the reason she ended up having A Day in the Limelight chapter were she defeated The Dragon of Empresss Tyrania, the Big Bad of the Gargoyle Story Arc, to save her father herself, instead of ending up a team boss fight as originally intended. This also enabled the writer to give her more character growth and an excuse to Take a Level in Badass, so it worked out in more ways than one.
Bentley the crazy Adorkable hyena from the Rango fanfic Snakes With Guns is easily one of the most lovable OCs in the Rango fandom.
Child of the Storm, by the same author as the below, has quite a lot of these thanks to the author's penchant for reimagining characters, as well as throwing in those characters at the last minute, later developing them into prominent figures in the story. The two main examples come in the form of Carol Danvers and Diana of Themyscira, both of which were added in at the last minute, apparently entirely on a whim and praised as original takes on the characters. They've both grown from fairly minor characters into two of Harry's closest friends, two of the more badass characters in the story and bona fide fan favourites - in a poll of favourite new or reimagined characters, Diana was the runaway winner, with Carol being joint third behind (unsurprisingly) the Winter Soldier, who's even more of a Woobie than usual thanks to the sections from his perspective, and sharing third place with Huginn and Muninn. Indeed, Carol's grown into a full on Breakout Character, being close to a Deuteragonist with Harry, and she and Harry are now the Fan-Preferred Couple (with Harry/Diana being close behind).
On the villainous side of things, Gravemoss started out as a minor, creepy Necromancer who was the villain of a minor arc in Excalibur and included simply for variety. He quickly grows into a major league villain and a character that fans love to hate.
Jean-Paul Beaubier a.k.a. Northstar and Uhtred Ullrson. The former is a fairly minor member of the X-Men and the latter began as a minor OC Asgardian who was apparently set up to be The Rival to Harry. Both become two of his closest friends, with the former developing into a deceptively harmlessCamp Gay flirt with considerable Hidden Depths, the ability to pull off an absolute absent minded Sherlock Scan and be arguably the mostruthless of the kids in a fight, as well as being the Only Sane Man. Also, as of chapter 60 he seems to be this world's version of the Flash. Uhtred, meanwhile, is developed from a fairly Flat Character whose primary motivation was resentment at the attention Harry got simply for existing, while his hard work barely got him any, to (one shared Near-Death Experience later) Harry's loyal (if snarky) oathman and Sworn Sword, a major league badass who knows his way around an axe. Also, he and Jean-Paul are pretty much a de facto Battle Couple.
Sean Cassidy is added for the sake of variety to Peter Wisdom's Exalibur squad, but despite initial uncertainty by fans, grows into a popular mentor figure to Harry, something helped by his nature as an Adaptational BadassGrandpa, something helped by the way he gently reins Harry in when he looks to be going too far and the bond he has with Luna Lovegood.
In the The Wizard in the Shadows, Emrys Ap Derfel. Originally created, as Word of God admits, as an unintentional Expy of the author and of Harry himself - green eyes, difficult past, great power and destiny, something which has previously been lampshaded, he was surprisingly well received. Several plot developments, an epilogue and the start of a sequel, he's developed into a key member of the main cast and Word of God has hinted that he'll take over Harry's role as The Hero later on in the Expanded Universe.
Eirian and Miriel are given expanded roles in the sequel (the latter had merely been a throwaway reference before hand) and a third, Maglor is pure Spotlight-Stealing Squad.
Unfortunately, the series is now entirely composed of Dead Fic.
Yuuka Kazami of Imperfect Metamorphosis was growing to be such a focal point of the plot that the author ended up having to devote several chapters to a giant brawl between her and Yukari to take them out of the direct action for a while and realign the focus to Rin and Rumia. Being a maniacal, sadistic, overpowered gadfly tends to have that effect. Being a Great Old One doesn't hurt much either.
The South of Nowhere fanfic 'Romance on the Set' has one In-Universe on the show Spencer and Ashley star in. Rachel, a character played by Taylor Momsen was intended to be recurring, but gets promoted to regular due to her popularity and even becomes part of the Fan-Preferred Couple with the main character
The Bridge to Terabithia fanfic "Unearthing Secrets" has Conrad, the very British exchange student and Jesse's best guy-friend, due to his realizing Jess and Leslie want to be more than friends before even they do and making frequent and amusing attempts to cockblock Leslie's egotistical Romantic False Lead whenever he is able.
Prince Heins of Frozen Hearts, largely because he cares a great deal for his brother, Hans, unlike the majority of their brothers and even after everything Hans has done.
Donut in Dusk's Dawn, or at the bare-minimum he's the least despised character. Having one of the few somewhat competent voice actors probably helps.
The Bridge gave us a fanon example within a fanon example. Despite starring the A list names of various kaiju franchises and the roster of My Little Pony: Friendship Is Magic, one of the most popular characters with the readers is completely fan made and wasn't even made by the author. Blade Dancer was a Free-To-Use character on Fimfiction.net the author wanted to use for a single scene. Fans took to her moments of hilarity so much that Blade Dancer reappeared in subsequent chapters and is arguably the lead of the secondary cast.
Fiora, Gangrel's daughter, is well-liked for some unfathomable reason.
From the sheer amount of fan-requested Omakes about her in The Fifth Act, Yuffie. She only appears in a small subplot and as the punchline to a Brick Joke but the readers lapped it up. Probably because her scenes are the few purely funny scenes and because her Noodle Incidents are ripe for extra stories.
Initially set to be a foil to Zack, Kunsel's reinterpretation as a savvy Almighty Janitor won him the adoration of the fans. He gets as many Omakes as Cloud does.
Xavier, the reptilian Cyn'Taak, from Zelda's Honor is a very popular one with readers. She is decribed as being very loyal and innocent but still highly lethal and dangerous. Her survival of the endgame events prompted a rather overjoyed response from one reviewer.
From Rose Of Pollux's Metamorphosis, we have The Piper, a Chameleon-arched Jamie. He's had positive fan reaction, a few pieces of fanart drawn of him, and will apparently be making a return soon.