Alpha and Omega has a few, but the most notable one is Lilly due to her cuteness and situation. She and Garth, another example in regards to his character development and terrible howl gag, are sometimes preferred over Kate and Humphrey, to the point of some fans becoming concerned that they'll disappear in the sequels. (Which they did.)
Marie from Disney's The Aristocats has gotten a huge load of attention from Disney and cat lovers over the years. especially in Japan, she was exclusive to Tokyo Disneyland in the mid 2000's, until she started making appearances in Walt Disney World's Epcot and moved to the Magic Kingdom a few years later. Speaking of Japan, there was a spinoff manga called "Miyiya & Marie'' that was made in 2012 and released in Japan and Brazil where Marie is the main character. The manga later gained a US/Canada release on June 2018 under the "Disney Manga" brand. She's also featured the most in Disney merchandise and anything related to the film. In fact, there was going to be a sequel which starred Marie, but it got cancelled when Disney closed its animation studio.
Manolo's cousins, the skeleton bandita looking Adelita twins from The Book of Life, are popular for their design. Though their personalities also help.
The relatively minor character Morkubine Porcupine from Chicken Little has quite a fanbase despite his small screen time and only three lines of dialogue (They were "Yo", "No", and "Whoa"). He's also considered far nicer than most of the characters.
Foxy Loxy also seems to be rather popular, considering how many have complained about her HeelFace Brainwashing.
After the three mains, Bonejangles can be said to be the most popular character in Corpse Bride, and is often the subject of an alternate ship with Emily. Apart from his big song "Remains of the Day," however, Bonejangles is pretty much just an amusing background character in the movie. He never even gets a name on-screen. Being voiced by Danny Elfman helps a lot.
The Minions from Despicable Me, to the point of overtaking the main characters (Gru and his adoptive daughters — Margo, Agnes, and Edith). Needless to say, fans of the "mad scientist adopts cute orphan girls and learns to love them and consider them his family" plot were more than slightly irritated.
Smiler also seems to be pretty well-liked, if the amount of people (including on this very website) believing that she's the real hero of the movie and supporting her antagonizing of Gene is any indication.
Chernabog and his sequence, Night on Bald Mountain, from Fantasia. Everyone remembers the beautiful pieces of music from the whole thing, but this was the one that stuck to everyone's memory. Everyone that ever watched this was in fear and awe of Chernabog, the sequence is regarded as both so amazing and frightening that it caused the Slavic Satan to haunt many's memories to this day, and it should come as no surprise that, of all the things from Fantasia to put into Kingdom Hearts, they chose Chernabog.
Some of the few other characters who contest him for that popularity are the Shark trio (avertingEverything's Even Worse With Sharks) and the seagulls. All three showed up when Walt Disney World's EPCOT park decided to add the Finding Nemo characters to its The Seas aquarium— the gulls appear in animatronic form outside, Bruce educates kids in a section dedicated just to sharks (despite not having the space for any actual sharks), and Crush hosts "Turtle Time With Crush".
Frozen: Even though he was originally thought to be The Scrappy before the film's release, Olaf the Snowman has been praised as the best Disney sidekick since Timon and Pumbaa.
Mambo from Happily N'Ever After. A cute, purple, awesome, wisecracking, sarcastic cat from a rather mediocre animated movie. Even people who hate the movie love him.
She appears for less than two minutes in the film and has only one line (apart from loudly inhaling), yet still manages to upstage Carol Burnett, Jim Carrey, andSteve Carell. Katie from the CGI Horton Hears a Who! is a perfect example of this trope. As well as The Mayor's son, JoJo.
Ruffnut from How to Train Your Dragon, despite having only a few lines and sharing all of her scenes with the other secondary characters. She's aroused by insanity, that's always hot! Being voiced by Kristen Wiig certainly helps.
The trio of Humming-Fish from The Lorax are this, as well as Cy, the O'Hare delivery guy. The latter in particular, as he only appeared on screen for less than three minutes of the movie's entirety!
The penguins from Madagascar, to the extent that they earned their own spin off The Penguins of Madagascar, and that spin off got a movie of its own! Be honest - did you see Madagascar as a film about friends moved from a zoo to the jungle with a few scenes based around penguins, or did you see it as a film about penguins that kept being hijacked by that idiot zebra and his friends? On a similar note, the zoosters get severely upstaged in the third film by the circus trio- or more specifically Vitaly.
Tamatoa, the giant crab from Disney's Moana. He only appears in one scene, but his catchy yet creepy Villain Song, "Shiny", makes him quite memorable.
The Princess and the Frog has Charlotte who is utterly beloved despite her supporting role. Not only does she help Tiana achieve her dreams by paying her a lot of money to cater a party, but when an accident happens and Tiana ruins a plate of food, Charlotte accepts it as an accident, takes Tiana upstairs, and gives her some of her own clothes to wear since hers were ruined. She subvert everythingyou'dexpect from a beautiful rich girl.
The Secret Life of Pets: Snowball is really the show-stealer even though he is a supporting character. Though being voiced by Kevin Hart could have some effect on it.
Sinbad: Legend of the Seven Seas has Eris who, despite being the villain, has very little screen time. Through Evil Is Sexy and her gorgeous character design, alongside her interesting personality and powers, she is very popular in fandom, to a point that many only watch this movie for her.
An interesting case occurred during production; the three fairies were originally intended to be minor supporting characters, with no names and no differences between them other than the colors of their clothes. The filmmakers became such fans of the characters as they developed that they wound up taking over the film. They even go on to become supporting characters in Sofia the First.
In Who Framed Roger Rabbit, the Toon Patrol fanbase makes up an astonishingly high amount of fans, right after Jessica Rabbit then Roger Rabbit. They don't even get named on screen. They don't even survive the movie and they still get the Draco in Leather Pants treatment in fairly equal quantities.
From Wreck-It Ralph, Sour Bill is very well liked, but even more impressively is Turbo, aka King Candy's original identity. In fact, he got his own t-shirt on ThinkGeek (which is unfortunately no longer available) before the site sold any other merchandise from the movie, even of the main characters. Something has to be said for that. Being voiced by a graduate of Joss Whedon productions Dollhouse and Firefly probably helped with the geek cred.