Sokka and Momo accidentally get strung out on peyote for a day and a night in the desert. Inevitably, Sokka was afterwards forever depicted by fans as the go-to character for any Mushroom Sambas. Probably because as soon as he recovered, he licked something off a cave wall.
Katara: You've been hallucinating off cactus juice all day, and you eat something you found on a cave wall?
Sokka: I have a natural curiosity.
Aang's kiss screw-up in "The Ember Island Players". He kisses Katara once, she doesn't want it, and instantly a certain subset of fandom has decided he's an entitled "Nice Guy" who doesn't care about Katara as anything more than a prize and doesn't deserve to be the hero or have any girlfriend.
In the Sequel SeriesThe Legend of Korra, Mako will forever be the guy who heartlessly strung Asami along, and then made out with Korra without bothering to break up with her (there actually was a breakup scene, but it was quick and done without dialogue, so that's how it looked). It's helped by his portrayal in season 2, as a big part of the problem was the show not properly acknowledging what a huge jerk he was to Asami, so when he does the same thing again, he ends up humbled and admitting he was wrong.
Suyin scarred Lin's face when Lin broke up a robbery Suyin took part in, which their mother Toph covered up before sending Suyin away to live with her grandparents. It was an accident that she immediately regretted (and in fact is the only aspect of her quite checkered past that she's explicitly shown regret for - or does she?), but Lin is such a popular character that for many fans, this was enough to label her a lifelong criminal who Lin never should have forgiven.
An arguable example is the Optimus Prime deaths. Each incarnation does die once or twice, and that's once or twice more than most characters who aren't from superhero comics, but you can't say "he's died a million times" unless you treat all Optimuses (Optimi?) as if they were the same guy.
Ultra Magnus is only remembered by fans for the infamous movie line, "I can't deal with that, now". Not only has it become an internet meme, but it also forever painted Magnus in fans' minds as an arrogant and lazy commander who would rather pass off responsibilities to his subordinates than actually get his own hands dirty. The fact that he's seen coordinating strategies more often than he is executing them doesn't help matters much, but he is more proactive than this misconception paints him as being. On top of that, the original line was said as he was in the middle of trying to pilot a ship that was crashing, so it was less "Who cares?" and more "Kinda busy here!"
Also, from the Transformers Movie, Ultra Magnus "usurps" leadership of the Autobots to the point of insisting the Matrix be merged with his spark. "Evidence" of this is shown by the fact that the Matrix only glows in the hands of Hotrod, but because Ultra Magnus is the de facto leader at the moment, everyone just ignores it.
Remember how G1 Red Alert was always panicky and ultra-paranoid? If so, that makes one of us: In the aptly-named episode "Auto Berserk", when a missile hits him in the face, resulting in brain damage that would have killed him eventually, he starts acting in this manner, to the point of helping Starscream get his hands on a superweapon just to keep the Autobots, whom he believes have turned against him, away. He's fixed later. Fans seem to forget both that he was this way for one episode only due to damage, and quite how dangerous the paranoid schizophrenic Red Alert really was. Even his toy bios go on about his paranoia, as if something we've never witnessed in any episode or comic but the brain-damage situation was in fact his defining trait.
A mild case of Older Than They Think: Toy bios were written (and often toys released) in advance of the characters turning up in related fiction and sometimes bore little resemblance to how the characters were portrayed in the cartoon or comic (Ratchet is described as a party animal, for example). Red Alert's paranoia was used for his Day in the Limelight episode but treated as a temporary state of affairs and ignored elsewhere.
Mix-Mix-Mixmaster's Verbal Tic of re-re-repeating the beginning of a sentence... some-some-something he only actually did in one ep-ep-episode ("City of Steel"). Thank-thank-thankfully. Shrapnel, however, really did repeat the last word of every sentence almost every time he appeared, appeared.
Beast Wars once had a damaged Waspinator think he was Shrapnel... only to start talking like Mixmaster did in "City of Steel".
Sentinel Prime may be going this way due to Transformers Animated, due to his smug attitude, general disrespect for others, and sometimes morally reprehensible techniques. In later continuities, there are some aspects of it, one of the names Zeta Prime has, suggested by the writer of Exodus is Sentinel Zeta Prime, and demonstrates much of the same behavior. The Sentinel in Dark of the Moon seems to avert this. But then it turns out he's worse than the Animated Sentinel, using both sides of the conflict and murdering Ironhide.
Hot Rod/Rodimus Prime probably would have been the Replacement Scrappy in any case, given how beloved Optimus was, but he really didn't help his case by being partially responsible for Optimus' death, distracting him at a critical moment, with fans insisting he did it deliberately. But with how it went down, while Hot Rod could have done a better job of helping if he hadn't intervened Optimus would have died anyway.
Transformers even provides a meta-example: Transformers Animated came to a rather sudden end for various reasons. According to some fans, this means that Hasbro loves canceling things and produces shows, comics, and toys for the sole purpose of abruptly canceling them all. Any series people like is met with comments of "wonder if it'll get to episode/issue 10 before Hasbro pulls the plug on it?" and occasionally people ask whether a toy has been canceled after it's already out.
An in-Universe example occurs in Animated with Bulkhead continually bringing up the fact that Professor Sumdac was, well, deceived into rebuilding Megatron.
Tygra in ThunderCats is known as a weak-willed junkie, despite being addicted twice, only one of which was actually presented as a drug.
Aquaman is commonly haunted by his portrayal in the Superfriends cartoons; as a guy whose only real powers are swimming and talking to fish he was (almost) always useless, to the point of Memetic Mutation. This has actually worked out for him a little, as lateriterations of the character usually go to great (and awesome) lengths to subvert this image.
Unfortunately for Aquaman, this image of him continues to perpetuate via parodies of him in other works, most notably Mermaidman and Barnacle Boy in SpongeBob SquarePants.
Wendy broke up with Stan exactly once, in the seventh season of South Park. They got back together in the eleventh season finale and have been together ever since. Yet fanfic writers tend to portray Wendy as a manipulative shrew who breaks Stan's heart again and again. This is usually done to justify Stan leaving her for Kyle. But even some writers who like Wendy latch onto the idea that she and Stan break up and make up all the time.
It may have more to do with the fact how shallow their relationship is shown at times. Both have shown heavy attractions to other characters in an extremely unsubtle manner (Stan once constantly attempted to make passes to a substitute teacher and even gloated about supposedly making love to her to Wendy's face while Wendy became disinterested in Stan in favor of another popular jock less than one season after they got back together). Their less than affectionate relationship was even Lampshaded in Raisins.
In Teenage Mutant Ninja Turtles fandom, April O'Neil's yellow jumpsuit, her fucking jumpsuit. Honestly, every conversation about the old show dissolves into one about her hotness and jumpsuit, this has even made it into other adaptations, as a reference or actually happening (Hell, in the Back to the Sewers season of the 03 show, she wears one!).
On Codename: Kids Next Door, Lizzie used a "Boyfriend Helmet" on Numbuh 1, and ordered him to destroy his teammates. In several future appearances, she was developed more, given her relationship more depth...but people's minds were already set. She became the single biggest target of Die for Our Ship in the fandom. Admittedly, she remained clingy, but nowhere close to that level.
Total Drama Island: Ezekiel made one sexist comment during his short time on the island. Two seasons later, even though others have shown far more sexist tendencies, Zeke was pretty much labelled a Straw Misogynist, and is still hounded for it.
Gwen- both in-universe and out- will never live down being kissed by another girl's boyfriend. That one scene led to Gwen getting voted out and all her allies abandoning her, (Sierra even referring to her as the 'New Heather) even though she'd been a good friend and strong competitor up till then. In All-Stars, she is placed on the villain team entirely because of this, and becomes their Token Good Teammate.
Starfire of Teen Titans was shown drinking mustard once. It's common for it to be referenced in fan works. She is, however, shown at several points later with a bottle of mustard with a straw in it in the background, even if she's not actually in the process of drinking it.
Spider-Man: The Animated Series - whole show, for the censorship issue. Yes, they couldn't say "die" or "kill," have Morbius suck blood, or have Spidey full-on punch anyone. But it seems that's all anyone says about it lately. In fact, it was an ambitious arc-based series with a lot of depth, emotion, surprises, and the portrayal of Venom that has impacted every adaptation since. Interviews with showrunner John Semper reveal that as it was on Fox - yeah, thatFox - it was a 24/7 battle to keep it that way. And just because they couldn't say "die" doesn't mean no one ever did die.
Professor Farnsworth from Futurama, having been declared dead as a tax dodge some years before, found himself irritated that his son Cubert used this fact to perform a hostile takeover of Galaxy Express.
Farnsworth: You take ONE nap in a ditch and people start declaring you this and that!
And of course, Leela's infamous one night stand with Zapp Brannigan is mentioned every time Zapp makes an appearance in the show. Usually by Bender or, more commonly, by Zapp himself.
Sym-Bionic Titan: Xeexi got his Memetic Molester status by mind raping two characters in an episode. Only one instance is really ever noted, but now Xeexi is only remembered as a rapist, even though he's also a tactical genius, and well... dead.
Fluttershy wanting to be a tree, based on a random night conversation on a train. This received a Continuity Nod in "Hurricane Fluttershy" where she hides inside a tree costume to avoid participating in the local pegasi's efforts to supply Cloudsdale with water.
Fluttershy's Sanity Slippage in "The Best Night Ever" forever convinced a large section of fans that she's secretly a Yandere.
A Meme in which Scootaloo is secretly a chicken, based on a short bout of teasing from her friend Apple Bloom.
Pinkie Pie being a sadistic serial killer who may or may not have severe childhood trauma, based on her Sanity Slippage in "Party of One", compounded by a certain infamous fanfic. Never mind that in the episode she was, at most, bipolar and manic depressive, which are many times more likely to result in self-harm than any violent tendencies.
Celestia is often depicted in fan works as an arbitrary and capricious dictator.
Before that, she (and Luna, which no-one seems to remember) turned Discord to stone... after he conquered Equestria and turned it into a nightmarish World Gone Mad. Naturally this led to depictions of "turn it to stone" being her answer to every problem that can't be solved with "send it to the moon". (Funnily enough, Discord seems to think this In-Universe. "Unlike you, I don't turn ponies to stone!")
Rainbow Dash said "twenty percent cooler" once, and "ten seconds flat" twice. To a lot of fans, they might as well be her Catch Phrases.
Twilight will never live down her Sanity Slippage (noticing a pattern?) in "Lesson Zero". In fairness, it was terrifying. However, not only did Twilight have some basis for Sanity Slippage in "Swarm of the Century", but she did it again in "It's About Time". Furthermore, she is slowly learning to control it as of "Games Ponies Play". The fans have spoken about her mental health, and the writers are listening.
Shining Armor did a Fastball Special with his wife Cadance exactly once, in a life-or-death situation where there was basically no other option. (And it worked, saving Spike from certain death and the Crystal Empire from enslavement by King Sombra.) Since then, the fandom only knows him as "Wife Thrower" (albeit affectionately).
Lyra Heartstrings has once been seen sitting on her haunches (like a human would) on a park bench in "Dragonshy". Since then, you can't swing your arm without hitting a fanfic, music video, comic, or some other fan work depicting Lyra as a human-obsessed fanatic, bent on proving humanity's existence, gaining hands, or becoming human herself.
Sweetie Belle gained a reputation as The Ditz because she didn't understand "more than I can chew" was a figure of speech.
"A Canterlot Wedding" has many examples of this:
Twilight accusing Cadance of being evil despite having no evidence (though she was right, just not in the same context she was thinking).
Shining Armor yelling at his sister, more or less cutting off his ties with her, and never apologizing for it after Chrysalis got kicked out of Canterlot.
The Season 3 premiere featured a villain who was intended to be a sinister and ominous presence in the vein of Sauron, but whom many fans interpreted as being an ineffective Orcus on His Throne. Sadly, poor Sombra will never get to redeem himself in the eyes of the fandom, as he is the only villain on the show to have been Killed Off for Real.
The episode "Feeling Pinkie Keen", in which writer Dave Polski worded the ending so badly that it turned a perfectly acceptable "Just because you don't understand it doesn't mean it doesn't exist" moral into sounding more like "Science Is Wrong and you should just accept that things work the way they do without trying to understand it". Before "The Mysterious Mare Do Well" this was the episode that was negatively spoken about constantly, although later it was finally able to be Lived Down.
Merriwether Williams' debut episode "The Mysterious Mare Do Well" is still a top contender for the show's worst episode. Her next episode, "Hearth's Warming Eve," was better received, but then "Putting Your Hoof Down" and "Dragon Quest" were again controversial and cemented her reputation as the worst writer on the staff who has no understanding of the characters, despite the next season's "Wonderbolt Academy" showing that she's definitely learned from her mistakes. This is best illustrated by the response to her episode "Bats," which was accidentally credited to Meghan McCarthy. Response to the episode was very positive at first, but when the word came of who really wrote it, a lot of fans suddenly turned on it just because of her.
Princess Cadance dropped the ball and went right down to the Scrappy status she had been rescued from for not inviting Spike, one of the key figures in saving the very empire she rules, to the preparations for the Equestria Games. Notably, she did eventually Live It Down in the episode "Equestria Games", where she invited Spike to light the torch at the opening ceremony - and later the fireworks at the closing ceremony, giving up her own place to do so.
Soarin the Wonderbolt had his first real debut scene in the season one finale: "Best Night Ever" where he enthusiastically purchases and apple pie from Applejack. This resulted in many fans flanderizing him into being some kind of pie-addict.
Applejack's Gen 1 counterpart was made famous for being the subject of a song in a My Little Pony cassette tape from the '80s which is about her being a "silly pony". The silly pony trait has been projected onto the current gen AJ by fans (note that FIM AJ is somewhat accident prone and goofy, but no more so than nearly every other pony in the slapstick heavy series).
In X-Men: Evolution, Scott was always a nice guy to everyone unless they deserved otherwise. However, he and Avalanche had a known rivalry due to leading opposing teams, usually Avalanche instigated it, and mostly Scott was defending someone else or simply reacting. However, during season 2, Avalanche had changed. Not as in he developed, but his personality had completely taken a U-turn as he was suddenly in love with Kitty and willing to join the X-Men simply to be close. Obviously, Scott remembers how he's acted and doesn't trust him. When Avalanche proves he's not interested in learning at the institute Scott retaliates by reactivating the Danger Room control for a second to make him trip up, a complete Out-of-Character Moment (he made a joke, completely forgetting whothis is). And when someone starts stealing the X-Vehicles, Scott, as well as EVERYONE thought it was Avalanche. When its all over, Scott apologized for this and offered to start again. Lance decides to quit because, after his time here, he's realized its too much work and not really him. However, the Brotherhood fans and a few others refuse to think of Scott as anything but a petty jerk who, without reason, just hates Avalanche who is nothing but a saintly loving Boyfriend to Kitty (despite that by the end of this season he returns to previous characterization and breaks up with Kitty), and that Scott was the reason he quit, having driven him away with his bullying and accusations when Avalanche would have made a great addition to the team. Sigh. That's two characters remembered for a personality they didn't have, because of one episode and one Out-of-Character Moment.
Similarly, the New Recruits are only remembered by some fans as idiots who only want to cause trouble and if left alone would destroy the world. They only did two stupid things, steal the X-Vehicles, and break into the Danger Room unsupervised. Not only did they learn their lesson, they actually showed they were smarter than previously thought (how many of you could fly a jet or survive a Danger Room session designed for the more experienced children?), in fact, it wouldn't have been a problem had Avalanche and Kitty not got in the way and caused the systems to get fried and fired at two Air force jets. But because one caused Avalanche to quit and another was 'confirmation' people always think of them as Too Dumb to Live assholes.
Many characters in The Simpsons are constantly lampshaded by the things they did in the past (especially the secondary characters). Some character only become known by the things that happened to them.
Meanwhile, more prominent characters in the series have past status quo changes lampshaded around them. For instance, there is Apu, who is now currently defined by his marriage to Manjula, his eight children, and his affair.
Thanks to an unexpectedly widespread Memetic Mutation, many people will remember Groundskeeper Willie solely for calling a group of French students at Springfield Elementary "ya Cheese-Eating Surrender Monkeys!" It's the one thing he has ever said about French people, derogatory or otherwise, and longtime fans of the show will tell you that Willie has contempt for people of many different nationalities, including his own. ("Damned Scots! They ruined Scotland!")
As for Lisa, occasional references have been made towards her vegetarianism and Buddhism, both of which were made permanent into order to get celebrities Paul & Linda McCartney (3F03) and Richard Gere (DABF02) to make their one-episode appearances in the respective episodes.
Lisa is also well-known for her profile quote "Embrace nothingness!" from the arcade game despite her saying this only once in the actual show.
Then there's Seymour Skinner, who has been referenced by his false identity, as well as his relationship and break-up with Edna Krabappel.
The town of Springfield as a whole will probably be never forgiven for driving Bart to kill himself in "The Boys of Bummer".
In-universe example: In a Robot Chicken skit on G.I. Joe, a new recruit is given the name Fumbles after slipping on his spilled soda. This leads him to defect to COBRA for the sake of revenge. Unfortunately for the Joes, "Fumbles" happens to be a Badass BookwormCold Sniper who is capable of single-handedly killing them all. Even better, at the end of the sketch, Cobra Commander is so impressed that he wants to give the sniper a much better nickname, only for him to coldly respond "It's Fumbles. It's always been Fumbles."
DreamWorks Animation is having a very hard time living down the creation of the so-called "Shrek genre" that was popular in the 2000s, which led to their Dork Age from 2004-2008 that ended up cementing their reputation in the public consciousness as "that one studio that makes fun of Disney and rips off Pixar". Unfortunately their dork age seems to have also been their most successful period - while their films have overall been doing better critically since they managed to pull out of it, financially their movies have been doing worse, leading their stigma in the public eye as "the Shrek guys" to remain.
Disney is still constantly mocked for all the direct-to-video sequels they churned out, even though they stopped making them after John Lasseter took over.
While it's understandable since "When you wish upon a star" is basically the theme of the Disney company, Disney Animated Films are often generalized into only promoting that moral (that a princess, or any person, just needs to want something and they'll get it). The Princess and the Frog seems to address this prevalent idea, and balanced it out with a hard work moral.
The same applies to the idea that all classic Disney cartoons are generally bland and cutesy stuff. Yes, there are a lot of cartoons in the Disney canon that fit that trope, but Uncle Walt and his studio also made a lot of impressive technical innovations in the animation business. Look at all the details and realistic atmosphere in films like "Snow White", "Pinocchio", "Fantasia" and "Bambi" and compare that to the art of most other animation studios, and a lot of the early Disney cartoons from the 1930s and 1940s have scenes that are pure Nightmare Fuel, almost on the level of a horror movie for adults.
It's been two years and they're still complaining about Winnie the Pooh being released the same day as the final Harry Potter film, calling it a sign of Disney's declining faith in 2D animation, though it did moderately well in the box office (making up its $30 million budget) and Disney said it lived to its expectations.
Most of the classic cartoons from the 1930s until the 1950s have a reputation for being nothing more than violent slapstick with a lot of explosions and people hitting each other. Despite the fact that the Bugs Bunny and Daffy Duck cartoons, for instance, are very dialogue driven and a lot of comedy also comes out of the dialogues between the characters.
For that matter, the Censored Eleven are disproportionately referenced in media, even though they comprise less than 1% of all Bugs Bunny cartoons.
Superboy in Young Justice has yet to lose his Emo Teen label, despite the fact that he grew out of it after the first ten episodes and lost it completely in Season 2.
Well, he was still a little emo in season 2, albeit for different reasons since the subplot of Superman refusing to accept him got swept under the rug his angst was re-directed towards a very ugly breakup with Ms. Martian.
Superman being a stubborn, insensitive Jerkass towards Superboy throughout the first season, even though season 2 depicts them as having buried the hatchet on the matter lack of character development doesn't help.
No matter what Brian from Family Guy does that might redeem himself, certain fans will never forgive him for vocally espousing his ultra-liberal viewpoints, particularly in the episode "Not All Dogs Go to Heaven."
In Ed, Edd n Eddy, despite showing some Character Development, albeit smug and a follower, Jimmy will always be known for framing the Eds in the episode "If It Smells Like An Ed."
Similar to the Mixmaster example above, Roadblock from G.I. Joe is known (and frequently mocked) for his Rhymes on a Dime dialogue; while he did talk like that, he didn't do it all the time. However, most parodies of the character make him say every sentence in rhyme, as if he always did.
One season 2 episode of Superjail! depicted the Twins as cannibalistic, insect-like, and also consuming bleach and other toxins. Even though some of the alien traits depicted in it were not referred to again in the following season, the episode definitely left a mark on fans' minds and fanart and comments will mention them in some way. For some, the episode seemed to ruin the characters and exaggerate the alien nature a little too much. And then you have the fans who claim the characters should never have any fans that like them over the actions they pulled in the episode.
Alice, er, "assisting" the Mistress in the season 3 premiere goes down this way for other fans. Never mind whatever else Alice did before or after that episode, there are some that give her the reputation of "Ruined Warden/Mistress foreverand is in the way".
Hey Arnold! an in-universe example, one episode had Rhonda throw a party in which some characters were not invited for being Geeks. They bring up the literal definition of the word, which repeatedly prompts this exchange: "...And none of us bite the heads off chickens! Except Curly." "Yeah! And that was only the one time!"
The latter character of Tom and Jerry frequently gets flak with fans due to the handful of episodes in which he is a Designated Hero who defeats Tom despite starting the feud. This disregards that Jerry was usually genuinely benevolent (or at least more so than Tom) and arguably one of the most vulnerable heroes to the loss of Karmic Protection in Western Animation, not to mention a similar number of occasions Tom got the last laugh despite still being the instigator. This is best illustrated in The Itchy & Scratchy Show, where the two main characters are blatant Expys of Jerry and Tom respectively. The show's portrayal of the Jerry-like mouse character is that of a sadist with a penchant for murdering not only Scratchy but any other cat that happens to appear in the episode. The opening sequence shows that the violent roughhousing is meant to be an equal rivalry, but there have been few if any episodes to support this.
Itchy And Scratchy were in fact stated by Word of God to be based more on the far more violent Herman And Catnip shorts, yet another Follow the Leader to Tom And Jerry that helped Flanderize the one sided sadism of the cat and mouse dynamic.
To a lesser degree, nearly all slapstick animation associated with the Karmic Trickster formula (especially in the Golden Age era) is believed to be revolved around a tall order Disproportionate Retribution method, with the protagonist being a self righteous little masochist who heckles, brutalises and just acts ten times crueller than the "villain" throughout the entire cartoon over a very minor slight at the beginning of the story. This is despite the fact that many series (the better written ones at least) actively tried to ensure their heroes look provoked. Warner Bros in particular were rather wary of Bugs Bunny turning from a mischievous trickster into a bully, going through an endless number of increasingly malicious antagonists that could look repugnant enough against him, and even having Bugs lose odd shorts he acted up to completely debunk the Double Standard.
Dana Tan, Terry's girlfriend in Batman Beyond, is best known for constantly breaking up with Terry and is also often called a Damsel in Distress who's constantly getting rescued by Terry/Batman. In fact, while she's often mad at Terry, she only broke up with him once; except for that one episode, they're always still a couple, not in an on-and-off relationship. On the Damsel in Distress front, she only has to get rescued in one episode and is briefly in danger in the movie, and neither time does she passively wait for rescue.
In-story, Terry is constantly reminded of his delinquent record, despite having spent months in juvenile hall.
Onion from Steven Universe is seen as evil by a lot of fans because one episode showed he steals tickets from arcade machines and another had him wreaking havoc with Pearl's replicator that Steven traded him for a toy that it turned out he stole from Steven in the first place.
Tumblr was quick to latch on to a brief scene in the Clarence episode "Clarence Gets a Girlfriend" where Jeff expresses resentment over not being able to get a girlfriend because he's a nice guy, sounding a lot like "nice guys" who only act nice to girls because they expect to get something out of it.
The Flintstones will probably be remembered infamously for shilling cigarettes in their early days.
Aardvark: I hope none of the other anteaters saw that. Ooh, I'd never live it down!
Thomas the Tank Engine tends to get flak from many fans over odd episodes that display Fantastic Racism towards the diesels (particularly in Misty Island Rescue, a feature length episode which is generally considered poor in every other quality anyway).