Originally just a mention in the Whateley Universe, Aquerna has become this trope. She's one of the least powerful students at Whateley Academy, and became popular enough that one of the Canon authors is now writing Aquerna stories too.
The Queen of Rogues and Robbers was originally supposed to be a one-shot villain in The Questport Chronicles, but has been brought back every year due to her popularity.
Mabaka! has Maruchi, Rokuro's magic teacher. He was almost certainly designed to be a major prick, yet most readers can't help but love him.
In Worm, a character appears once, in the midst of a crisis, a fat superhero who is named only in passing as Chubster, as the casualties are tallied. He remains unconscious throughout his appearance; the protagonist tries her hand at CPR, fails, and she abandons him to die. Despite his unglamorous nature (or because of it?) and lack of dialogue or action, he is repeatedly referred to in the site's comments section, appears or gets a mention in numerous pieces of fanfiction, and is part of several in-jokes among fans.
For Tumblr's 2016 April Fool's prank, they held a parody of the year's elections. Decision 2016 had users vote between four lizards for...something. Each lizard had a basic personality and a blog to use as their platform. The candidates were Ricky, Deborah, Mop, and Wretched Tooth. Mop and Deborah were instant hits with the users, who quickly provided tons of posters, speeches and ads for their favorite candidates. By the end of the event, Ricky had about 6 million votes (though the counter jokingly edited it to 2 votes), Wretched with 8 million, and Mop and Deborah having about double that. Mop ended up winning, with over 14 million votes.
Ellen Baker became an overnight sensation on Pixiv and Twitter, an especially impressive feat considering she originated from a textbook. Her internet presence first went viral when a Japanese user tweeted pages from his brother's 2016-19 edition of New Horizon (a long-running English language textbook series for junior high classrooms) and commented on its surprisingly animesque illustrations and attractive character designs, most particularly of its blonde English tutor. Being a dorky Gorgeous Gaijin, moeteacher, Ellen Baker proceeded to lead an explosion of fanart and R34 images, and many overseas fans professed a desire for similar characters on their own textbooks. Even the original artist took notice, appreciating Ellen's newfound popularity but worrying that her purpose as an instructor would be derailed.
New Guy, from this webcomic has garnered a large collection of fans, painting him as an All-Loving Hero and a symbol of positivity and empathy. Most people saw him as far more sympathetic than the protagonist.