A lot if this happened as adaptations of the Slayers light novels were made, namely the anime:
Lina's sociopathic tendencies were born in the anime and carried to manga adaptations, and her sociopathy (and apathy towards regular people) only gets worse as each season passes. While's she's a bit greedy and can over-react sometimes in the original books, she was not sociopathic at all, and, more importantly, she did not abuse her magical powers (i.e the Dragon Slave spell) the way she did in the anime. She is also more abrasive towards her allies as the anime goes on as well.
Gourry got the worst of it; he goes from merely being a bit tactless to being borderline mentally retarded - his memory is so short-spanned that it's miraculous that he can still get out of bed and function normally. Much like Lina, he was never that much of The Ditz in the books - in fact, while genuinely unaware of some things (such as magical lore), he acts dumb to tease or deceive others. Later manga adaptations, like The Hourglass of Falces, thankfully revive that aspect of him. The Evolution-R anime also managed to give him back shades of his former competency.
Amelia had a love of justice that was both an odd quirk yet an honest belief in the novels; the anime and manga flanderized this to the point that she could see nothing gray about anybody; she's also significantly dumber to boot, to the point of being The Chew Toy. The newer anime actually tones all of these down, but some other stories crank up her enthusiasm and giddiness to compensate.
Zelgadis did not change much initially, save for becoming snarky, but as time passed, he became more of a whiner and, despite, well, whining about his chimeric body so much, he takes joy in Insult Backfire that occasionally happens to him, tends to dismiss his companions (especially when they're trying to be actually nice to him), and in later manga and newer anime seasons, shows signs of being an Insufferable Genius. In the original books, he's a genuinely sad figure that simply wants to be normal again and atone for working under Rezo, the Red Priest.
Some of Xellos' more malevolent aspects are turned comedic in the anime (such as his tendency to spook others). Also, Sylphiel is not as demure in the novels as she is in the anime and manga.
Azumanga Daioh has a veritable boatload of flanderization in the manga. The Anime versions of the characters are the end result.
Kaorin's crush on Sakaki, though the series is arguably too short and Kaorin's crush simply less-discussed in the early stages for it to be a classic case, but it's still plenty discussed enough to get a shade creepy.
Osaka starts out as a somewhat slow-witted and eccentric, yet generally still well-adjusted girl, but becomes weirder and creepier as the episode count goes up. Most people agree this is an improvement.
In the manga version, Dororo is a Technical Pacifist who nonetheless has amazing ninja skills and doesn't ever shirk from the cause of justice, often playing the Only Sane Man to the rest of his squad. The anime exaggerates his pacifism to the point of often making him meek and indifferent to events, his opposition to his squad's schemes manifests itself more in the form of half-assed protests that eventually just alienate him from the others, his maturity is spun into an annoying emo personality, and in general he either plays the Butt Monkey to the other Keronians or isn't even there with them a lot of the time.
Giroro originally just had a soft spot for Natsumi. By Season 2, he is completely obsessed with her well-being, that he'll go into Knight Templar mode against his own commanding officer if he should do anything to harm her. This doesn't exactly help take over a planet.
Panda in Shirokuma Cafe. In the manga, Panda could be lazy and a bit thoughtless at times. In the anime, Panda has had these traits kicked up to eleven, to the point where it's a mystery how he still has any friends. Not a very gradual case either; right away from episode 1 Panda's situation was changed from already knowing about Shirokuma Cafe and getting a job of his own volition, to being so lazy he apparently had never even ventured across the street, and being forced into getting a job by his mother. For the most part, any scene that features Panda being nice (his Tanabata wish, helping out at the Summer Festival) it's from the manga, and any scene that features Panda being borderline mean (taking away Llama's job out of jealousy, making Handa bike in the rain for his phone) it's anime-only.
Yuuna's jealousy in Maburaho got Flanderized to the point that, though she was originally very bland, she actually became an entertaining character.
Shuichi's hyperness and Tohma's obsession with Eiri (which starts out as merely protective and gets creepier over time) in the Gravitation manga. The anime has more stable characterizations, though skipping over most of the character development in the later volumes.
Pretty much everyone in Tenchi Muyo!, especially Ayeka and Mihoshi. Especially in all the "expansion" series. The characterization gets more and more flanderized the further away from the OVAs you get.
Takamura's not-so-sudden (de-)evolution from a skilled and respectable boxer into a Jerkass in Hajime No Ippo. He's always been portrayed as a Jerkass outside of the ring, but there's a limit...
Makoto in School Days transforms from a merely sex-curious teenager into an uncaring, womanizing bastard. Furthermore, the two main female love interests get reduced to only being known for their obsession with Makoto. Though Kotonoha may have been emotionally unbalanced from before,. However, it's shown in the second to last episode Makoto actually realizes he became flanderized and tries to fix things. Only to commit a critical mistake and be brutally murdered.
Kawachi. He started out as a talented baker with "real person" problems and a tendency to need to have the hero's eccentricities explained to him (and thus the reader). Over the course of the volumes this degenerated into him becoming a total Butt Monkey, suffering any indignation or humiliation that the other characters were apparently too cool to have happen to them, and a tendency to shout disbelief at any tiny thing, causing others to mock and ridicule him. It finally culminated in even his beloved mother and younger siblings being dismissive of his abilities, and as the series went on he became the equivalent of Krillin hanging out with Goku and Vegeta... only without the abiding affection and/or small amount of respect those two gave Krillin, as Kawachi's "friends" took to using him to literally waste the opposing team's time.
Also Kuroyanagi. At first, he was shown as a cold hearted judge with very high standard of food, but later is portrayed as a literal bread zombie whose only passion is eating delicious breads.
This long-running comedy manga contains some of its medium's most pronounced examples of the trope. Kasumi went from a normal Yamato Nadeshiko to an unfazeable near-parody. (Considering how comparatively dull she was before, it could be considered an improvement.) This is also applied to Nabiki's love of money, which propels over time from a merely opportunistic character to an appallingly two-faced exploiter. The first time Akane cooks in the series, it is merely bad and she realizes why immediately after tasting it (she made an honest mistake with ingredients, 'sides she's just a beginner); later in the manga, her cooking has become all but poisonous, she doesn't care what she throws into it, she refuses to taste it or to acknowledge that it tastes bad, and everyone else treats it like toxic waste.
Genma starts the series genuinely caring about his son (including going out of his way to help Ranma keep his curse hidden), despite being a selfish idiot who tends to do more harm then good with some very warped ideals and morals. By the end of the series, his already-extreme faults get flanderized to being willing to throw away his son for a knick-knack he already knows has little value.
Pokémon - By mid-Hoenn many recurring characters are little more than walking collections of running gags, with Brock arguably getting it the worst, with the Team Rocket trio close behind.
Ash, the main character, is noteworthy in that he started out as an Idiot Hero mainly due to his immaturity rather than him being an actual idiot. As he's matured throughout the show, but the writers still want to keep his idiot traits, his Idiot Hero status is due to him being honestly mentally challenged. His Oblivious to Love trait is one of the most noteworthy: compare his early release of Butterfree because he knew full well it wanted to mate with a female and make babies to a more recent encounter with a Cottonee with the same problem, whom Ash thinks just wants to "get a best buddy".
Pani Poni Dash!: Just about everyone ends up having one of their traits exaggerated to extremes (which is typical for its sub-genre). Three obvious examples are Mesousa's uselessness, Himeko's super-high level of hyperactivity (maho), and Kurumi's plainness.
Jaken, Sesshomaru's henchman from InuYasha, started out as a sadistic and very competent evil sidekick who occasionally wound up the butt of humor at his expense, and later on became a goofy weak klutz who often messed up his master's plans.
Minako from Sailor Moon, in order to distinguish her from Usagi (who was actually an Expy of Minako in the manga), was made more ditzy and less mature as the anime went on (compare her introduction in the first season to how she's acting by the last), which is actually a reverse from the manga, where she became more mature and intelligent as the series progressed.
It can be hard to believe, but Sanji wasn't always quite such a loser when it comes to romance and women. He was never all that successful in romance (unless you want to count those 20 bounty hunter chicks that were probably just leading him on) and was kind of awkward around Nami from the start, but it wasn't nearly as pronounced as it is now. His attention to the main females more often seemed kind of sweet, and he didn't quite come off as a dorky pervert like he does now. However, Oda gradually turning him into a full blown Chivalrous Pervert (coupled with epic Butt Monkey tendencies) was actually a really positive change. In retrospect, there was a period of time where he seemed a little too perfect compared to other main characters, and was in need of a serious personality flaw in the same vein as Luffy's flakiness and stupidity, Zoro's lack of sense of direction, Usopp's cowardliness, and Nami's greed.
Amusingly enough, back in the Kuro arc, Zoro and Luffy arrive late to the battle, but it's Luffy who got lost due to his lacking sense of direction, Zoro simply got stuck in grease.
Zoro has undergone a good deal of this as well, being both far more intelligent and level-headed in early chapters, but after Loguetown he began the steady descent into the mostly-clueless meathead he is today.
And now after being on Okama Island for so long, Sanji's become utterly weak against women. Once again, tropes arenot bad.
Though, said über-weakness has been the topic of Lampshading by Chopper, saying that his rocket powered nosebleeds, which require blood transfusions afterwards, are getting annoying and that he needs to be rehabilitated. With pictures first. This has actually become a significant plot-point, as Chopper now needs a donor to conduct a blood transfusion on Sanji after he spurted most of it out when meeting a society of actual, non-Gonk Mermaids. The Mermaids and Fish-men refuse to provide blood for a human, however. A useful trope indeed.
Higurashi makes rather entertaining use of this. When the show takes a break from all the drama and horror, more comedic and lighthearted moments often make characters act in a hilariously different way from their usual selves. Keiichi, usually a positive, optimistic charismatic boy who cares about his friends, becomes either Keiichi the Overreacting Prank Magnet or Keiichi the Brainless Perv. Dutiful, level-headed Mion becomes Mion the Tomboyish Leader. Rena, who is affectionate and friendly if a little... dangerous, gets all obsessed with things she considers cute (and taking them home). Satoko becomes a hyena-likeprankster and Rika is just cute and helpful.
Of course, this has somewhat dark twist for some of them. Keiichi acts that way because he became extremely stressed from taking studying too seriously and takes Dumb Is Good to high levels, Rena thinks happy days are limited due to her parents' divorce and acts as wacky to make the most out of them and Rika is Really 700 Years Old.
Shaoran went from a male Tsundere with comical deredere qualities on occasion to a meekDogged Nice Guy by the end of the anime's run. Granted, this may have been due to the new object of his affections now being the title character, but even when Sakura wasn't present he seemed noticeably more timid and underconfident than before.
A strange aversion with Kero's big form, that was initially depicted as more serious minded and gallant than his Sleep Mode Size. He gradually became goofier and more childish as the show progressed making the two forms of the character more interchangeable.
It's worth noting that the Cardcaptors dub toned down a lot of the exaggerative traits of the characters and made the dialogue and voice acting more 'down to earth', albeit often because they were relevant to plot points they didn't want to translate (especially in the case of Shaoran).
A minor character, Keigo Asano, falls victim to this. He starts off being a goofy and slightly neurotic kid who hangs around with Ichigo. In his appearances after the Soul Society arc, he freaks out at the drop of anything even resembling a hat. He's even worse in filler.
Aizen might actually count as an Invoked Trope. He's already close to being the single most powerful, intelligent, omnipotent character in the series......he just wants to be more so.
In Claymore, #22 Helen was originally a mature, serious, but lighthearted Claymore, but in later volumes her lightheartedness was exaggerated to Plucky Comic Relief proportions and she began acting like something of a child who needed Deneve, her Blue Oni, to keep her in check.
Belldandy in the original manga Ah! My Goddess starts as a character who is divine (of course), good-hearted, and a genuinely nice person but who is not above the occasional eye-roll or violent expression of rage (mostly towards Urd). As time went on she became more and more passive and sweet to almost saccharine levels. This is also illustrated by the progression of the different anime (OVA, movie and TV shows) which was made at various points in the manga's history. Best example: in the manga Keiichi works himself almost to death to get a ring for Belldandy and she reacts (at first) with anger at him beating himself up. In the same story adapted for the TV Series, she just cries.
In the manga and Brotherhood, Solf J. Kimblee weaves a happy line between monster and Magnificent Bastard, managing to pull his fair share of both awesome and horrible moments that leaves the reader/watcher unsure what to really think of him. In the 2003 anime version, much of this background had yet to be revealed so he was reduced to a stereotypical Mad Bomber obviously meant to be hated.
Similarly, Basque Grand was originally an unknown due to dying before his introduction. The 2003 anime cast him as a Colonel Kilgore character who everyone was happy to see die. The manga later depicted Basque as being one of the more reasonable officers during the Ishvallan Massacre, willing to kill a superior officer in order to avert unnecessary bloodshed.
Ciel Phantomhive in Black Butler season 2. They seem to only focus on his bad parts, making him seem much more evil.They also made him a lot more dependent on Sebastian than in the first season, making him more of a damsel in distress when he could have been capable of handling himself a little easier.
In the anime adaptation of Rosario + Vampire, almost every character gets hit with this:
Completely rampart in the Edolas (mirror world) versions of the anime characters. They have literaly one trait showing how they're different from their Earthland counterparts, and every single thing they say shows us this one trait.
This shows up in filler a lot as well. Gray is all Juvia talks about, and Fried is unable to make a simple decision without wondering how Laxus would handle it.
Much more obvious with Mizuki, who had a yandere gag that was used rarely in the first season coupled with wanting to see the protagonist in drag. The second season has this as her primarily character trait. She also gets better over time.
The characters of Fate/stay night and Tsukihime are prone to being flanderized in sequels, such as Kagetsu Tohya really playing up Kohaku's craziness or Fate/hollow ataraxia doing similar things to the likes of Saber or Tohsaka. However, Carnival Phantasm has taken these depictions and ramped them up even more resulting in a near stalker Akiha, a moe caster who acts like a schoolgirl and even more exaggeration of Ciel's love for curry. Arcueid and Taiga, on the other hand, act completely like normal while Ilya's sociopathy is greatly downplayed. Carnival Phantasm was made like that on purpose for comedy, though.
The anime turned Sakura Haruno into a violent psychopath who's constantly punching Naruto (and sometimes Sai) into the ground for the slightest infraction. While she does hit him a few times in the manga, the anime takes it Up to Eleven, and in the manga, it mostly stops after the time skip, while it persists in the anime.
While Hinata is just shy in the manga, she's much worse in the anime, stalking Naruto from afar and going red and fainting more than once when he makes the slightest amount of contact (physical or otherwise) toward her.
Sai. note He was brought up in a secret black ops organization known as 'root'('foundation' in the english anime), and was taught to not show or have any emotion whatsoever—only care about your mission. When he is put in Team 7 as Sasuke's replacement, he is socially akward and often unintentionally insults people due to a general lack of social skills. In the manga and anime he starts out pretty bad, angering Naruto in particular by insulting his manliness a couple of times, and calling Sakura ugly when trying to think of a nickname. However after a few missions with the team he begins improving and is seen reading a book on social skills. The anime however takes this to the extreme by having his relationship with Team 7 improve overall, while simultaneously increasing his social akwardness. He's now so socially inept that Naruto actually thinks Sai is hitting on him, when he actually misreads Naruto's actions as a sign of fear and tries to "show him tenderness." There's even a scene where he tries to spoon feed Naruto who has a broken arm. Sai's reading habit has also been given a huge upgrade*
in the manga it's like a one time thing meant to show that he's trying to form good relationships with others
, and he's seen in a library multiple times surrounded by stacks of books. Unlike in the manga, his reading habits tend to make his social interactions worse (99% of his bad interactions happen because he "read it in a book"*
which at one point in the anime is implied to be Make-Out Paradise, Jiraiya's infamous porn novel
Ino Yamanka at first started out as a ninja who focus more on her appearance and love than actual fighting. However, she still isn't above giving up those 2 to win (as evident by cutting her hair short to outsmart Sakura). She is also known to have the highest grade out of the Konoha 11. However, when the anime fillers kicks in, she was turned into a character who only cared about her appearance, where she freaks out when a prince chose another girl over her, and majority of the Shippuden's Extra footage containing her is about her complaing or glorifying her bust size.
Shinnosuke himself, or rather his butt. He's been mooning everyone for years, but ever since halfway The Noughties he suddenly Took A Level In Ass and flashes it all the time, speaks about it often and is far more proud of it he ever was, and "worse", he can perform amazingly well in pretty much anything that involves a tool if he holds said tool with his buttcheeks.
Masao is a bigger coward, Tohru's Closet Otaku tendencies overtook most of his character, Nene can't seem to talk about anything other than playing house, and Boochan only thinks of rocks.
Shinnosuke's mom Misae used to be mildly reasonable even if strict, but she became much louder and angrier. His dad Hiroshi used to get some respect, but now he's a giant Butt Monkey. Those facts likely have no relation, but who knows.
Some strange forms of this happen between mediums of Revolutionary Girl Utena; when Kozue is introduced in the manga (which ran side-by-side with the anime during their original release dates, despite technically coming first), her obsession with Miki is remarkable, scary, and more visible than it is in the anime (which is no less disturbing, but the main difference is that she's not clingy). Juri was the Alpha Bitch in the manga, smitten with Touga, and was jealous of those who got close to him; while she becomes an Ice Queenquestioning her sexuality in the anime, her manga traits go to Nanami, which get taken Up to Eleven. Bear in mind that not only does Nanami's love for Touga go to a sexual level, but she's also his sister.