Miss Koizumi Loves Ramen Noodles: Koizumi prefers to eat and wear the same things every day, appears very expressionless, withdrawn and almost never speaks to anybody, and when she does speak, all she ever talks about is ramen.
For example, during their first visit to the TV World, he sees nothing wrong with Yosuke, in the midst of a Potty Emergency, dropping his pants and relieving himself against a wall, and even asks Chie why he would want to stop him from doing so.
When he and Yosuke are knocked into the water for making perverted comments about the girls, he continues to have a complete lack of facial expressions, while Yosuke is simultaneously laughing and flailing about.
He has a rather odd habit of agreeing to random comments made by the other characters, regardless of their seriousness.
Yukiko: The next time he creeps me out, he's ash! Yu: Sounds good.
He also has a tendency to not react at all to absurd situations, and to be way too into certain antics of the more... eccentric members of the investigation team. Case in point: While the other characters are freaking out about the implied size of Naoto's chest, he and Kanji hang back and have this gem of a conversation:
Yu: Aren't you even the least bit curious, Kanji? Kanji: Huh? About what? Yu:Naoto, big melons or not. Kanji: Huh? Why are you asking me? I didn't look at her tits, I swear! Yu: Okay. Kanji: But that chick, she is pretty amazing. Yu: Which chick? Oh right, Funbags.
Aya from Shibariya Komachi is a Softspoken Sadist, admits he doesn't really have emotions, and feels no sympathy for others. He reveals he has started to feel some emotions due to magical bonding with the others in his group, but otherwise just does as he's told. He often will tell facts coldly in dangerous situations if he's safe instead of saving his friends, and sometimes even strangles them from behind for fun.
Yuuki Rieko of 14Juicy displays a limited emotional range and seems to have no interest in, or aptitude for, anything but soccer.
Shin Kazama only speaks when absolutely necessary and has a blunted affect. He's socially awkward, as seen with how he interacts with Ryoko in flashbacks. He's aloof and detached from the other pilots at Area 88, and only slightly less so with friends such as Kim and Mickey. He demonstrated this behavior before his time at Area 88, so it can't be attributed to depression or war trauma.
Mickey has a somewhat bipolar temperament. He can be cheerful and gregarious in some situations, and extremely angry at other times. He's prone to violence, as demonstrated when he punches Makoto Shinjou in the first episode and beats him within an inch of his life in the last episode. It's not clear if this is Mickey's default personality or a result of his war trauma.
While a great number of the cast from Attack on Titan has several mental issues, special mention should be made of the main character, Eren Yeager, considering that even if in his early years he grew up in one of the most stable and loving environments for the setting: Even as a child he was prone to uncontrolled anger outbursts, had difficulty socializing with other children (his only friend was Armin, another awkward boy), constantly himself got into fights, and he stabbed to death two adult men as a child, granted, they were human trafficker kidnappers who had previously murdered Mikasa's parents in right front of her. His rationale for doing it? "I killed some dangerous animals. Animals who happened to look like humans". Later events through the series have not helped his sanity very much.
Generally Played for Laughs, but the extremely strange behavior of most of the cast of Axis Powers Hetalia coupled with how they've lived through countless years of wars, diseases, and other difficult times makes one wonder.
Osaka from Azumanga Daioh thinks in ways so completely different from other people that it's easy to think she might be mentally disabled in some way. She's dreamy and inattentive, prone to weird misunderstandings, has poor motor control, and occasionally seems to suffer from actual hallucinations. But although she seems mentally slow, she gets only slightly below average grades at a regular school and manages to socialize more-or-less normally. She even has some Genius Ditz tendencies: she's prone to penetrating insights that escape all the other characters, she's surprisingly well-versed in some obscure topics like marine biology, and her odd way of looking at the world makes her extremely good at certain kinds of riddles. The joke here — which can easily escape Western viewers — is that Osaka's spacey, laid-back personality makes her a humorous inversion of the stereotypical brash, loudmouthed, Hot-BloodedIdiot from Osaka.
Claire Stanfield from Baccano!. There's definitely something off about him, though it's hard to pinpoint exactly what. He's prone to violence but follows a set of rules so completely alien to the average person that he can't really be called "good" or "evil", and can be affable and calm, even while brutally murdering someone. He's even said that he believes the world to be an illusion and everyone to be a dream of his own making, which is often attributed to sociopaths, and thinks of himself as completely invincible (which might even be true, thanks to Achievements in Ignorance).
Bakuman。: Eiji Niizuma has extremely odd sitting patterns, demonstrates some trouble with social conventions and nonverbal clues, and has an obsessive interest and talent in a particular subject.
Although incredibly intelligent, Edogawa Ranpo can't complete daily tasks like taking trains or going home alone without guidance, and at times has no common sense at all. He also doesn't really care one way or the other how things go, unless he has proper motivation. Before Fukuzawa took him in, he could neither understand social norms nor get along with other people, causing him to be kicked out of every job he got, and gradually became severely disconnected and isolated from humanity.
Edward from Cowboy Bebop is ludicrously intelligent but shows absolutely no ability (or inclination) to socialize in a remotely normal fashion for even brief periods. She almost always skips, cartwheels or dances instead of walking, and she sings improvised songs about whatever she's doing, often as a substitute for normal conversation. Her closest friend is a hyperintelligent, non-talking dog.
Super-detectives L and Near have several odd tics and habits and a near genius intellect that highly suggest some manner of disorder, though nothing's ever spelled out in the series.
Villain Protagonist Light Yagami is also undeniably insane, but it's never clarified where exactly it comes from. Between his monster god complex, inability to cope with any perceived evil, and constant manic laughter, there's something definitely wrong with him; that's all without even discussing the fact that he picks up mass-murder like a new, exciting hobby. For the record, Word of God states that the reason Light went off the deep end was because he was a perfectionist and couldn't reconcile that with the fact that he had unintentionally murdered someone except through Insane Troll Logic.
Hattori Heiji's really thick about other people's feelings, bad at picking up social cues, and extremely awkward a lot of the time. He can't lie without stuttering and giggling like an idiot, and he latches onto ideas or interests and does not let them go. For example, when he first became friends with Conan, he talked about Shinichi SO incessantly that his childhood friend believes him to have a girlfriend in Tokyo with the last name Kudo. He's also extremely adept at remembering little details and noticing anything out of the ordinary, no matter how minor.
The protagonist, Shinichi Kudo/Conan: In the first episode, he does not know when to stop rambling on about Holmes and Conan Doyle and talks to Ran about it the entire time they are at the roller coaster. Even whenever he dates her and starts off wanting to tell her his feelings, instead he ends up gabbing about Holmes again. He is not very social and it is implied that many of his teachers and classmates believed him to be arrogant and self-absorbed. Also, he seems to be quite blunt and unaware of social tact.
Maria, from A Devil and Her Love Song, is shown to be incredibly blunt, has great difficulty in expressing her feelings, and shows an immense lack of social tact, namely bringing up topics that make other people very uncomfortable or upset and not realizing it. In flashbacks, this is shown to have been normal for her since she was a small child, with her mother worrying that it would cause trouble for her later in life. She shows little restraint when it comes to lashing out at others (she was expelled from her first school for hitting a teacher who didn't take a friend's bullying seriously) but also goes to great lengths for and clearly cares about people close to her. Personal attacks and harassment on her, meanwhile, are generally met with emotionless responses.
Considering how quirky most of the characters in Eyeshield 21 are, the fact that both Shin and Tetsuma are both considered a little "off" by both the other characters and standards of the series says something:
Shin speaks in monotone with textbook level formality, has an encyclopedic knowledge of everything related to physical fitness (he maintains a VERY strict nutrition plan and seems to be very well-read on human anatomy), and absolute devotion to improving himself as a football player. At the same time, he speaks his mind in the most direct way possible (both positively and negatively), has no interpersonal skills or awareness of social norms (he doesn't see anything wrong with walking around shirtless), and is completely oblivious about anything that's not football or school-related (when his teammate Sakuraba grows a beard, gets a crew-cut, and starts training harder, the only thing Shin notices is that Sakuraba's muscle tone has improved). Nonetheless, he's very respectful and always means well, so the few friends he has seem to take his many idiosyncrasies in stride.
Tetsuma is very literal-minded, even more oblivious to social norms then Shin (as well as being an expert on his position), and can't seem to function normally without his best friend to tell him what to do. When he does speak (which he'll only do if someone specifically tells him to speak), it's very robotic and formal. Most likely because of his difficulty in interacting with people, he dearly treasures his friendship with Kid, who accepts him regardless.
Erza Scarlet from Fairy Tail is extremely socially awkward and serious, and holds other people to such high standards that she tends to drive them away. Much of this can be explained by her traumatic childhood and the fact that she hasn't been very well socialized with other people.
In Free!, if it weren't Played for Laughs Haruka's obsession with water and swimming, to the point that he once attempts to dive into a fish tank after stripping down to his swimsuit in a pet store, would almost certainly result in someone trying to diagnose him with a disorder. He's also extremely socially awkward, rarely emotes at a normal level, and is very blunt when interacting with others, which isolates him from most of his peers. While he gradually improves his social skills over time at the beginning of the series he's almost entirely dependent on his friend Makoto, who makes sure he actually goes to school and communicates for him.
Ren has some sort of intense codependency focused on her husband Akira — so much so that years after his death, she remains intensely hostile to the point of extreme emotional abusiveness toward any female character she saw as a rival for his affection, including her own daughter. This seems reflect insecurity over classissues in their relationship — Ren was a lowly maid before the head of the household fell in love with her — but her behavior is so extreme that it's hard to believe she wasn't a bit unhinged even before; at one point, her response to feeling as if her "mind is very clear" is to take a knife and threaten her own child with it, to get back an empty box. The most we're told is that she's "a little sick, mentally and physically", but no specifics are given.
Akito shows similar behavior. Intense co-dependency towards the other Zodiacs (to the point of having a complete breakdown at the thought of any of them leaving) is just the tip of the iceberg. Akito has also been known to physically and mentally assault anyone who threatens what she considers to be the happy little world the Zodiac all live in. She has no friends outside of the Zodiac, and those relationships are awkward and strained. While more than a little of this is likely the result of Akito's abuse at the hands of Ren, it's also hinted that Akito inherited some sort of mental instability from Ren and/or Akira.
Machi seems to have some sort of disorder, too, although it's considerably more subdued than Akito's or Ren's. She has no friends (except her half-brother), dangerously low self-esteem, and trouble communicating with people in general. And then she feels compelled to ruin things when they're too "perfect", either methodically or in fits of violence. Presumably this is because of all the stress and anxiety that she built up trying to be a "perfect child", all compounded when her parents essentially declared her a failure and shifted their affections to her little brother.
Shu Ouma from Guilty Crown is an Extreme Doormat with No Social Skills who admits to himself that his mind might be out of step with everyone else's, and has only made "friends" by going along with what other people say. When he makes a carelessly cold remark about someone else and is reprimanded for it, he can only think about his own feelings that were hurt, rather than feeling bad about what he said. He also has trouble with making eye contact with other people.
Erio from Ground Control to Psychoelectric Girl is a delusional teenage girl who believes she's an alien who can fly. For the entirety of the first episode she's rolled up in her futon and even walks around in it. She also has shown dangerous behavior trying to "prove" that she's an alien. Erio starts the series as an Emotionless Girl and a hikikomori until Makoto coaxes her out of her shell. Her behavior is due to having gone missing a year prior and having no memory of the six months she was gone. Erio has since become convinced she's an alien.
Gugure! Kokkuri-san: Kohina is very intelligent and level-headed for her age, but has a very peculiar way of speaking, shows severe emotional detachment and is convinced she's a doll rather than a real person.
Several protagonists in the Gundam franchise have traits like this. Seems to have something to do with being a Newtype:
Amuro Ray of the original Mobile Suit Gundam is capable of social interaction, but absolutely hates it. He's paranoid, prone to focusing on himself, and in his Establishing Character Moment, is shown sitting in his room in his underwear, not having eaten in a day, looking at a computer chip through a microscope and studiously ignoring the evacuation siren blaring outside. His friend Frau specifically states that this isn't uncommon behavior, and that his neighbor was supposed to come in and tell him if the siren was going off.
Kira Yamato of Mobile Suit Gundam SEED shares many of Amuro's personality traits; the main difference is that he tries to be social (despite sucking at it) while Amuro deliberately avoids other people at all times.
Tiffa Adill from After War Gundam X is a Mysterious Waif who in the beginning largely keeps to herself and fixates on creepy drawings she makes to express her emotions, wears loose-fitting clothing that looks like something a girl with sensory integration issues would wear and demonstrates a form of Spider-Sense in additional to more explicitly supernatural Seers abilities. The fact that she herself questions whether she's really a Newtype makes it even more ambiguous.
Mikazuki Augus from Mobile Suit Gundam: Iron-Blooded Orphans is extremely quiet and rarely shows any kind of emotion on his face or in his voice. Whether happy, angry, or sad, his voice and expression are always perfectly level. He also kills with zero hesitation, and seems to outsource all of his agency to his friend Orga Itsuka: no matter what Orga orders, Mikazuki will do it, and it is rare for Mikazuki to decide to do something on his own. What's scary is that flashbacks show that Mikazuki was like this even before he became a Child Soldier; the very first scene shows a young Mikazuki with a gun in his hand over a bleeding corpse, asking Orga what it is he should do next.
Hime Shirayuki/Cure Princess from Happiness Charge Pretty Cure seems to suffer from sensory overload issues when more than one person tries to speak to her or when she hears loud music. A Running Gag in early episodes is that she usually becomes overwhelmed to the point that she physically flees the room when in these types of situations. She also displays a general lack of knowledge of how to behave in most social situations.
Eru Chitanda of Hyouka gets easily distracted and has an outright obsession with mysteries, and isn't able to stop thinking about them until she solves them. It's also implied she may have some sensory integration issues and seems to have much sharper senses than other people.
Shinji Inui of Initial D lacks basic social skills and understanding societal norms, such as failing to know why people would find his actions, like giving the opponent the lead in a race or ramming his car against theirs, deplorable. However, Shinji can memorize the most minute details of the Tsubaki Line, making him one of the most formidable drivers on the course, yet his meticulous behavior or interest in the subject is deemed unusual by most people.
Inside Mari implies this with the original Mari (as opposed to the protagonist-Isao-in-Mari's-body); when Isao tries repeatedly to tell Mari's mother who he really is her reaction is a strained smile and trying to get Isao to take medication. As the manga goes on there are heavy implications that no body swap occurred and Mari has a Split Personality. This is later confirmed.
Sawako from Kimi ni Todoke. At the age of fifteen she's never made a single friend, and frequently misinterprets social cues with hilarious results. She doesn't seem to find this at all weird. Though this is mostly explained by her frightening appearance causing people to avoid her and her resulting social inexperience.
Marginal #4's Atom Kirihara tends to obsess over things and get attached to rituals, schedules, and lucky charms; plus he's very loud and hyper, with little observance of social norms, leading others to call him the unit's "Wild Shooting Star". Played a bit differently as he is still an attractive, successful Idol Singer, and he and his unit make these traits into a positive, rather than a problem.
Buchi from Mekko Rarekko is quite the example: He knew as a kid that he's not as smart as the other kids, claiming that he's hopeless and hapless while being aware that his parents wanted him to be a normal child. Because of that he hated going to school, but he felt that if he didn't continue going to school that he couldn't become normal and that his parents would hate him for it. Because of all that, he never told his parents about how he was bullied and he just stayed quiet about it, leading him to developing a very small number of social skills. Later on, he takes up photography because he realized that his parents would see him as a good-for-nothing son and he wanted to be noticed. In the end, it didn't work and he believed that no one would ever notice or like him, which in turn lead to him tearing up one of the pictures he took and breaking down crying. He only got much better when Taishou noticed him and helped him out. Buchi then focused on making sure that Taishou wouldn't hate him, doing anything for him. Buchi goes to extreme lengths to make sure that his friends stay his friends and when it doesn't work, he wonders if he did something wrong or if there is something wrong with him.
Inspector Lunge. Absent staring, hand-tics, Spock Speak, socially clumsy, isolated, compulsively obsessive. It's especially weird that nobody ever mentions any possible diagnosis, considering the manga's protagonist is a doctor and several characters who are psychologists, though mostly of the forensic variety, also feature prominently.
One of the first things the audience learns of Shiro of No Game No Life is that she has a communication disorder. In Japanese parlance, that is a catch-all phrase that covers not only what is strictly the medical definition of the term, such as Speech Impediment, but also such things as social anxiety or autism.
The protagonist Tomoko from No Matter How I Look at It, It's You Guys' Fault I'm Not Popular! seems to live this trope. She's extremely socially awkward, to the point of being incapable of talking to anyone who isn't her relative or best friend without stuttering and stumbling over the simplest of words several times. She also seems to view herself as superior to other people for no good reason, often taking anime and manga clichés as her stepping stones to becoming popular but they generally end up failing. While the series is playing it for comedy at times, it gets Played for Drama just as often.
In The Pet Girl of Sakurasou, despite Mashiro's behavior, it's never outright stated that she has a mental disorder. The closest thing her dormmates did to name her a disorder was for Sorata to call her "special", having been fed up with her antics earlier that day.
Pokémon: Jirarudan/Lawrence III from Pokémon 2000. He's an art collector of a ridiculously high magnitude who seems to have learned social skills by rote, has a narrow and fixed attention span, wears a long coat with an undershirt to tropical islands in the middle of summer, has almost no change in facial expression or vocal intonation despite living by his passions, seems to have difficulty recognizing cues from others, and takes everything, including the legend and Misty screaming at him, only by the words presented without considering tone or alternate meaning.
Black is so focused on his goals that he needs his Munna to eat his dreams in order to focus on the task at hand. Attempts to do so without clearing his mind causes him to overload his brain and faint. He does eventually get a little better whenever White is concerned, but it still takes a lot of considerable effort. Black also has No Social Skills as a result of being so focused; he isn't inherently a Jerkass, but often he honestly just doesn't notice how his actions can inconvenience or hurt others.
Despite having high intellect and physical skill, Blake lacks emotions and has to memorize various manuals that tell him how to interact with other humans and Pokémon. He is willing to push a very damaged Genesect in order to unfreeze the Musketeers, and states that he doesn't understand how that is cruel — if Genesect gets hurt he will just heal it. He admits that concepts like "fear" and "pity" are unknown to him, shocking Whitley and Kelden.
Lillie's abusive mother has clearly taken a toll on her. She freaks out at being called "pretty like a flower" by Sun and is otherwise triggered by childhood memories.
The Nuns of Princess Jellyfish clearly have something, what with their singular obsessions, various tics, and near-total inability to interact with anyone outside of each other, but this isn't focused on and usually only pops up as a source of comedy.
Ami Mizuno/Sailor Mercury from Sailor Moon is incredibly intelligent, but has a hard time making friends or fitting in with kids her own age, and often comes off as cold and unemotional to her peers. This is even more pronounced in the live-action version, where she also displays a complete inability to understand sarcasm, hyperbole, or social cues (which is Played for Drama a few times). Ami also on occasion displays low self-esteem, and seems to have some form of social anxiety. A notable but ambiguous disorder attached to this would be her "allergy to love letters", where she actually breaks out in hives when she is presented with a love letter.
Nozomu "Mr. Despair" Itoshiki of Sayonara, Zetsubou-Sensei. Focuses on one topic for an incredible amount of time; depressive and paranoid to a nearly delusional degree (although it's Played for Laughs); is a self-proclaimed master of not looking people in the eye due to a family custom that would force him to marry the first person he makes eye contact with. The rest of his family have their own quirks and likely played a large role in making him the dysfunctional mess he is.
Yuki from School-Live! is an eccentricCloudcuckoolander who acts much younger than her actual age. She is delusional and is oblivious of the Zombie Apocalypse due to Repressed Memories, until being forced to kill a zombie snaps her out of her hallucinations. Miki thinks she has Multiple Personality Disorder, however her symptoms don't fit. Even prior to the zombie outbreak, Yuki was shown to have been bullied by some other girls due to her personality and looks (she wears a cat-eared Nice Hat and has a kiddie looking backpack) and as a result she had few peers besides her teacher.
Lain in her initial appearances within Serial Experiments Lain. She shows impairment in the use of nonverbal behaviors, has developed few peer relationships and the ties with two of her friends are very weak, does not show enthusiasm to seek enjoyment or socialization with others, and lacks social or emotional reciprocity. She also rarely speaks, and cannot converse well or start/hold a prolonged conversation. Finally, she becomes unusually enthralled by computer/technological objects and their construction as the series goes on. Never mind the loss of sense of time and space, vivid hallucinations(?), moments of amnesia, hearing voices... All possibly justified from being an Artificial Human. Or the Anthropomorphic Personification of the Internet. Or something. In the video game adaptation, Lain sees a therapist who diagnoses her with several disorders. Her Creepy Child aspects are also far more pronounced than in the anime.
Yutaka is a highly emotional and sensitive boy who is prone to Tender Tears. He also has sensory issues, but he's very skilled at singing soprano.
Vladmir is a prodigious boy soprano who has a sensitivity to sounds.
Saori from Wandering Son is an asocial Aloof Dark-Haired Girl who is moody beyond the normal pubescent awkwardness. She's shown to have not have any friends most of her life and goes near hikikomori once. She Cannot Tell a Joke, has terrible social skills, and is awkwardly blunt. When confronted with a friendship issue, Saori decides to ruin her 2-year friendships and avoid her former friends.
The character Satsuki Yatouji from X/1999 is a computer genius and one of the world's most dangerous hackers. In her personal life she mostly avoids contacts with other people (and is frequently annoyed by it) and spends most of her time connected to the supercomputer Beast. She is also extremely rational and seems to have problems with understanding human emotions.
Medaka and most of the other Abnormals in Medaka Box, by virtue of being a form of Super Soldier. Medaka herself, for instance, has no real personality outside of what she thinks people think she is. She never shows any kind of worry or unease, makes snap decisions about people that go against her friends' suggestions and tends to ape the poses of people around her when they show emotion. The show is mostly a parody of the God-Mode Sue, so it's usually Played for Laughs, though her odd behavior is a point of contention to Straight Man Zenkichi.
Bleach: Something is not right with Giselle's mind. She seems to have some disconnection with reality, as she genuinely doesn't seem to realize that performing Cold-Blooded Torture and receiving an orgasm while hearing the screams of someone she kills, makes her a sadist, as she denies being one. She likewise seems to have no problems with abusing Bambietta, even though she loves her, despite being much nicer to people she doesn't have the same affection for. It seems Giselle treats Bambietta that way precisely because she loves her. She can go from bashing Bambietta's head in a fit of rage to gushing and hugging her in extreme joy and proclaiming how much she loves her within mere seconds. And when Giselle looked at what she had done, she had a look of confusion in her face, as if she didn't realize what she actually just did. She also displays several control and abandonment issues throughout the series and that is without going into her necrophilic tendencies.
Ichimatsu is almost always monosyllabic, speaks in a deadpan tone, is seemingly depressed and has sadistic tendencies, which makes his family worry if he'll ever become a functional member of society. The only thing he seems to care about are cats. In an episode where the sextuplets' parents decide to get divorced, Ichimatsu blackmails his mom to get her to choose him to stay under her custody by saying he could easily become a murderer if left unsupervised.
Jyushimatsu is the polar opposite of his brother Ichimatsu: he's childlike, nonsensical, extremely hyperactive, has a goofy smile permanently plastered to his face and is obsessed with baseball, speaking almost exclusively using baseball terms. His brothers constantly wonder what "happened to him" to make him this way. Unrelated (or maybe not?) to that, he also has reality-bending powers that no one can quite explain, even in a surreal universe such as the show's.
At first glance, Iyami's obsession with France and insistence on saying he came from there seems like a harmless quirk, but the original manga reveals he's actually quite delusional. He's convinced he's French, to the point he eats using chopsticks as if they were Western cutlery and writes Japanese characters in cursive. It's even implied on a few occasions he wishes he could be... well, white. In one story where his assumptions about France are challenged by someone who has actually been there, Iyami has a severe nervous breakdown and speaks without his "accent" for the first and only time in the series.
Dragon Ball Super: Even before he falls off the deep end and becomes an Ax-CrazyKnight Templar, there's something clearly wrong with Zamasu. He fits many of the characteristics of a high-functioning sociopath, but he also has an inability to cope with any perceived evil, is extremely sadistic despite his "noble" intentions, and is incapable of even considering the possibility that he might be wrong. What makes him stand out compared to other villains in the series is that Zamasu wasn't born or created evil like King Piccolo, Frieza, Cell, and Majin Buu. He's supposed to be a god who overlooks the living world and give it guidance. So it's all the more jarring that he's so twisted, which is probably why Gowasu doesn't know how to deal with him.
Yu-Gi-Oh! VRAINS has two notable examples. The protagonist Yusaku lacks social skills is very blunt and direct and doesn't seem to realize that he comes off as rude this way; his emotions don't show on his face or body language even when he verbally states he is enjoying himself; and he has a tendency to list things in carefully ordered categories (of three), going so far as to stretch two ideas to fit three bullet points, while Aoi Zaizen, also known as Blue Angel, shows a lot of suspicion towards everyone outside of her online avatar and rarely shows emotions.
Fate/strange fake regularly suggests that both Saber and Flat Escardos have some sort of serious, untreated mental illness, and even the characters themselves readily acknowledge the likelihood. However, none of the characters have any sort of psychiatric background, and both Richard and Flat come from cultures where the field of psychiatry is all but nonexistent (Medieval Europe and a society of sociopathic luddite mages, respectively), so nobody is able to articulate just what they might have other than to say that Saber is "touched in the head" and that Flat is "a flat expanse with unintelligible scribbles on it."
The titular Goblin Slayer has very few people skills and an incredibly single-minded obsession with killing goblins. He doesn't seem to pick up on social cues and spent most of his time alone before the story starts.
The Witch, a member of the guild, has an odd cadence and seems to take a long time to speak, as evidenced by all the ellipses during her dialogues.
The titular Violet from Violet Evergarden is extremely Literal-Minded, incredibly blunt, nearly incapable of making any decisions for herself, incredibly attached to one person, and fairly emotionless. How much of this is her real personality and how much of this is due to howshewasbrought up is up to interpretation.
My Roommate is a Cat: Subaru is very uncomfortable around crowds and exhausted by basic social interaction, to the point of actively avoiding people as much as he can. He can also get hyperfocused on his work and reading to the point that he Forgets to Eat when deadlines come close.
My Next Life as a Villainess: All Routes Lead to Doom!: Katarina's family and friends pretty much all agree she's not normal by any stretch of the imagination, and they find it charming and frustrating in equal measure. She acts on impulse, is oblivious to subtext, can be spacey and absent-minded, is easily distracted, has difficulty with paying attention unless she's interested, has only a few things she's interested in trying to learn, frequently forgets or puts off her homework, isn't good at long-term planning, takes time to absorb information, seems immune to lectures, etc.
Besides the obvious social anxiety, Hitori Bocchi of Hitori Bocchi No OO Seikatsu displays a number of other quirks, such as trying to adhere to a literal script when hanging out with a friend, not being able to tell whether people are joking, and going into way too much detail about something off-topic. These traits are mostly used for comedy, though, so the possibility of her having actual psychiatric issues never comes up.
Lily of Wasteful Days of High School Girls has a pathological androphobia that manifests with hives whenever she comes in direct contact with men... and Tanaka. Her classmates speculate that the hives manifest out of her hatred of men, but a blind trial proves that Tanaka may be an exception to the rule and that the hives is not psychosomatic.
Keep Your Hands Off Eizouken!: Midori Asakusa is childish, tends to get lost in fantasies, has a strong attachment to certain objects (including a stuffed rabbit that she keeps as a Security Blanket, clutching it when overwhelmed or nervous), hyperfixates on certain topics, and displays such immense difficulty with being around strangers, especially in crowded settings, that she relies on keeping her friends around her at all times when she goes out in public. However, the story doesn't delve into any formal diagnosis, since it's primarily comedic.