Keiichi's father from Ah! My Goddess. He looks not unlike Andy Warhol. He shows up at Chihiro's shop and starts doing some work (having never met Chihiro before), speaks barely a word, and freaks out if a woman touches him or gets too close (the exceptions being his wife and Belldandy). When he freaks out, he silently runs to his motorcycle and races off — he's a skilled racer, even when he's going to the local pastry shop. He also defeats Sigel and Banpei outside the temple in hand to hand combat, no small feat for a mere mortal, just so he can get past them to say hello.
Shino Aizawa and her mother from Aizawa-san Multiplies. The former is regularly observed doing things like putting shoes on the wrong feet or completely spacing out, and her thoughts on developing a Literal Split Personality is that it'll help her become a comedian. Meanwhile, her mother seems more interested in the fact that Shino brought a boy home than the fact that her daughter can apparently now clone herself.
Hikari from Amanchu! arguably qualifies. She blows on a pea whistle everywhere she goes (including during class) and jumps from a big rock in a way divers jump from a boat—even though there's no water. Whether her mild flirting with Futaba, another girl from her class, is simply part of her off-beat attitude or perhaps something else is up to interpretation.
Finland from Axis Powers Hetalia shows signs of this; he thinks that "Blood-smeared Flower Egg" is a perfectly acceptable name for a puppy. Italy combines elements of this with The Ditz.
And Finland's first choice of names for the puppy was 'Go For It! Bomber!' Another suggestion was 'Sardine Picnic'. I wish I was making this up. In the Christmas Episode, the dog starts talking. Finland acts pretty nonchalant about the whole matter.
In fact almost every character can be one, like America trying to befriend whales (and succeeding).
Poland, hoo boy Poland. Lithuania even lampshades Poland's status: "I thought it was just one of your usual stories, that I can't keep up with, that takes place in your own special realm..." He could probably compete with Osaka in cuckoolander-ness at points.
Even England, normally the Only Sane Man, can get like this when it comes to the occult; he tries cursing America using a chair (at one point he nearly managed it, but when Russia sat in it he broke it by out-eviling it), and he makes friends with magical creatures like fairies and unicorns that only he can see.
Seychelles can be pretty spacey, ignoring France while he's talking to her and rambling on about fish, trying to play in snow as if it were sand, and asking Finland how to describe having ants everywhere.
Since these are anthropomorphic countries, they could just as well be called Cloudcuckoolands.
Ayumu "Osaka" Kasuga from Azumanga Daioh (see the page pic). She has a tendency to say and do strange things out of the blue, drifts off into daydreaming from which she is very hard to shake, and at one point apparently suspected that Chiyo's pigtails were detachable. Then there's the time she decided to wake up Yukari by banging on a frying pan with a wooden spoon. How she managed to grab a knife instead no one could explain, least of all Osaka (who wasn't fully awake at the time herself). She expressed mild astonishment. Yukari, well, didn't.
This may also be a generous part of why Mr. Kimura's wife is able to tolerate him—she can get so focused on a discarded soda can that she runs directly into a lamppost.
Not even taking into account the way he freely expresses his Comedic Lolicon tendencies, Kimura himself has such moments. For example when he walks into his classroom to find all his students having lunch, he apologizes and walks away backwards to the faculty room where he proceeds to have lunch himself... only to find out then that it's only 11 o'clock.
Fans of the series would doubtlessly recognize Chiyo-dad, the cat...thing. Who sees him the most? I'll give you a second to guess. Have an idea? Yes? Okay, were you thinking Sakaki? No. You were thinking Osaka, weren't you? Well, Sakaki sees him the most. Her tendency to bond with stuffed animals and the fact that she doesn't seem to notice that Chiyo-chichi was a dream makes some people think Sakaki is weirder than Osaka. Even Osaka found the "daddy hats" weird. Put it like this: Sakaki is weirder than Osaka when it comes to cute things and stuffed animals, but Osaka is weirder at everything else, and she's still pretty weird with stuffed animals too. Plush cities, anyone?
Another reason Sakaki doesn't have that kind of reputation is that most of the crazy stays in her head, only occasionally leaking out her mouth.
Isaac and Miria share a train of thought that has to be seen to be believed. For example, they once decided to steal a museum, building and all, for the sheer hell of it. Then they realized it was impossible... so they stole the door instead to stop people from entering. They plan a train robbery which "means going to the destination by train, then committing a robbery, then jumping on a train again to run away." Or the time Isaac decided to attempt to "steal gold directly from the earth rather than stealing it from the mafia". Through a process known to the sane as "mining", which he is convinced he invented. Did we mention that they thought bringing their friend a "little brother" as a surprise present was a fantastic idea? It also took them 70 years to realize that they were immortal. And they didn't actually figure it out. Their assumption was that they were reborn.
Graham Specter (wrench man) from the three bonus episodes goes on a long rant about tedium, to the point of attacking his partner screaming "death to tedium!" before doing a 180 claiming that "tedium is good" and gives him time to "think about things." That's when he's not taking cars and people apart with a wrench bigger than him. He comes off as a crazier mix of both Ladd Russo and Issac/Miria.
Yuichiro Tajima in Big Windup! is a baseball prodigy with expert peripheral vision and incredible accuracy when batting. When off field, he's borderline hyperactive, has the tendency to loudly discuss his masturbation habits and at least once almost stripped naked in public just to work on his tan.
I almost choked to death on a Dick Tracy watch once. In retrospect, I should not have eaten it box and all. But the bottom line is that communism is bad for your eyes. *beat* I mean television. I get those confused.
Orihime has an extremely overactive imagination which often sends her off on strange tangents that have nothing to do with the subject at hand. However, it also allows her to tell the truth about causing a fuss because people think it's just her imagination. She also combines ingredients in bizarrely inventive ways. As few people are brave enough to try her cooking, few know just how good a cook she really is. When she's asked to draw a picture of what she'd be like in the future, she draws herself as a giant, destructive robot in a futuristic, sci-fi world.
Similarly, Bobobo-bo Bo-bobo, in the show of the same name, while supposedly using a martial art based around his nose hairs, usually wins his fights by confusing the enemy into surrender. Then again, everyone on that show but Beauty likely qualifies for this trope.
You could argue that Beauty is the only character who qualifies. All the others are off in their own little reality, but she's normal and thus the exception. Beauty's the only sane girl of that anime. Gasser is fairly normal as well despite his bizarre fighting style, and Softon, while definitely weird in his own right, seems fairly sane. Bobobo, Don Patch, Jelly Jiggler, Dengaku Man, Torpedo Girl, and many of the villains all qualify, though.
Though not a regular Cloudcuckoolander, Makino from the manga version of Boys over Flowers has at least one time when she does this. In Volume 33 when she's given up on Tsukasa because of Umi, she compares her situation to the plot in The Little Mermaid (the real story, without the Disneyfication) and ends up ranting about how she doesn't want to become bubbles (or something to that effect) in front of her little brother who's very confused.
Ren Suzugamori from Cardfight!! Vanguard (before he was corrupted by PSYqualia). When introducing one of his long time friends to a new class mate, the friend asked to the classmate "What's your name?" and Ren answered with "It's Ren." The conversation continued with "No, his name *points to classmate* that guy." "I saw them write his name on the board and it was definitely longer than That Guy."
Run from A Channel. She even forgot to put on her panties to school. Her Panties!
Tomozou from Chibi Maruko-chan, Maruko's doting grandfather. He can sometimes do weird things that nobody understands, like imitate Maruko or that one time when he wrote "Work hard Japan!" on the flag Maruko was making for the white team for her school's sports day. There are times like when Maruko's sister was saying she doesn't use her head in class, Tomozou responded saying that when he puts on a "hachimaki" (Japanese bandana), he uses his head. Maruko seems to have inherited it to a lesser extent, with her strong tendency to daydream or to even go into a daze. There was one episode about how Maruko could be absent-minded and showed that Maruko doesn't know what she thinks about when she goes into a daze. Also, her friend Noguchi and definitely Noguchi's grandfather.
Kotomi from CLANNAD is very awkward, lacking all but the basic social skills, despite (or perhaps because of) the fact that she is a genius. She also tends to space out and come up with non sequitur responses, which she often combines with a deeply seated fear of bullies. Nevertheless Tomoya drafts her for the drama club, where her sweet and thoughtful demeanor makes her very popular with its members — as long as she refrains from playing the violin.
Perhaps justified in that Kotomi was traumatized by her parents' death, and she promised to do better and follow in their footsteps. She said that she'd read many books and that she'd become smart like them. With such motivation for Kotomi, it's no surprise that she lacks social skills when she's busy with what she promised her parents that she'd do. Various flashbacks in the anime show that she was already like this (kids avoided her because of her intelligence and Tomoya was her first and only friend). The death of her parents (and the fact that Tomoya avoided her afterwards) definitely made things worse, though.
Fuuko is also a total space-cadet. At one point she tells Tomoya she's warmed up to him, explaining that she likes him more than sea slugs (but not as much as starfish). Tomoya doesn't understand the rankingsnote Fuuko quite likes sea slugs, so this is actually a compliment in her mind. She tops this in the ~After Story~, where her behavior is very bizarre indeed, especially in response to Ushio's cuteness. She also tends to space trance out when thinking of cute things for long periods of time, only to snap out of it to finish whatever sentence she had started. She's in total denial about it, though.
Her never having any friends prior to Tomoya's involvement, being in a coma for years, and astral-projecting her wacky self into the school for most of that time probably have something to do with it.
Also Kappei, who is apparently incapable of remembering names or faces. And tells a touching story about a person he think he may love whom he lent his handkerchief... while talking to that same person. Also expects to be served tea during a job interview.
Code:Breaker has two: Nenene, who loves to randomly grope Cute Bruiser Sakura's breasts (and names them) and Yuuki, another Code: Breaker. Not only is Nenene Sakura's sempai, she's somehow a member of the student council. Her dad being the prime minister of Japan and head of Eden (the Code: Breakers' organization) probably had something to do with it. Yuuki, on the other hand is one of the most powerful of the Code: Breakers in The Organization due to his control of sound. For some reason, his nonsensical behavior annoys the usually lackadaisical Toki who happens to be Nenene's estranged brother. Naturally, Nenene is easily distracted as Sakura says "This is your brother!" while standing in front of a guy with the same hair and differently coloured eyes as her. To his (or his handlers') credit, Yuuki uses his nonsensical ideas ("He's a middle-aged mushroom suffering from depression") to become the chief of a multi-billion dollar toy empire, although all he really wants/needs are friends.
Ed from Cowboy Bebop. Though as a hyperactive teenage super-hacker, she also qualifies as a Genius Ditz. This may be hereditary, given how her father acts. Among other things, the man is dedicated to the goal of mapping out the newly altered terrain of Earth, a task which is explicitly stated as impossible due to the vast amount of debris still in orbit — any given map is only valid for two days, tops, before a new meteorite hits and rearranges things again. His favorite food is raw eggs sucked out of their shells, and he's such a skilled fighter that he effortlessly disarms Jet Black with a thrown egg, dodges Spike's kickboxing and knocks Spike head over heels with a single open-palmed punch. He instantly recognizes Ed when she makes an appearance, but is uncertain as to her gender and was the one who left her behind in the first place. While he rewards Spike and Jet with a big basket full of eggs as thanks for taking care of her, he immediately abandons her again to chase after a new meteorite crash-landing.
Shiro from Deadman Wonderland. Nobody except possibly her grandfather (who she ends up killing anyways) understands what in the world she's saying.
Jeri Katou from Digimon Tamers. This trope is depressingly subverted when it becomes less "Aww that girl's got a friend!" to her broken mind's only way to communicate in any functioning way... Yeah. And then she gets mind raped by an Eldritch Abomination.
A more straightforward example would be Mimi of Digimon Adventure who, unlike Jeri, never gets better, nor even once says anything that isn't noticeably, inappropriately casual or just plain out of place. By the end of season two, she still displays a sort of airheadedness that anyone on the planet would grow out of after so many near-death experiences.
Digimon Xros Wars gives us Blastmon who is more concern with keeping himself shiny and forgets that he is suppose to be fighting. The real kicker is when Cyberdramon latches itself to him to stop his attack he thinks its love.
In Dr. Slump the main protagonist Arale Norimaki is a robot without social programing. She's also hyperactive, extremely naive, enjoying the hobby of poking 'poop', has a complete lack of common sense, cause massive damage, want to have larger breast (despite being a robot) and tends to lift her shirt with no regard; doing so on one occasion simply to gesture as she asks Senbei if she can launch rockets from her chest.
Izaya Orihara of Durarara!!. For example, he once came across three girls attempting to bully a fourth. His response to this situation is to rant incoherently at them for a few seconds before announcing that while he does not hit girls, he does rather enjoy stomping on their cellphones. He then proceeds to steal the lead girls cellphone and stomp on it while laughing maniacally for a few second before stating that stomping on cellphones is extremely boring, and is no longer his hobby. At this point, the lead girl sics her boyfriend on him, prompting Izaya to pull out his razor blade and shave the man's head, though considering his status as a Troll, the clouldcuckoolander-ish behaviour was most likely deliberately invoked.
And Slon beats them all with this quote. "I'm not moving an inch until I've solved the mystery of the male nipples! This is my war!!"
Ellis who does things like bringing a rope to help Nadie out of a well, and then going down said well to personally hand the rope to her. Other examples including casually describing feeling the "incandescent flames of love" over a keychain and volunteering to help fend off a duo of gun-toting bounty hunters with a fork, and when she's turned down, pulling out a second fork and trying again.
Although the fork incident was a reference back to Noir, where Kirika first picked up a little fork from her and Mirielle's 'Mad Hatter's teaparty' with Chloe to use as a weapon. Later on, she kills Chloe with it.
Excel Saga: The main cast is an evil organization bent on city then World Domination, but do not have a concrete plan on how to go about it. The title character Excel is oblivious to the destruction she causes, how ineffective the group is, and how little her boss likes her. Their enemies are a group of disinterested civil service employees who do not care that they are saving the day, when they do not destroy a place themselves.
Juvia has permanent Shipping Goggles and is convinced that she is in a Love Dodecahedron. After all, since she's in love with Gray, surely every other woman must be too. Also, she celebrates the 413th day since she met Gray as their "anniversary" and doesn't understand why anybody would think this is odd. No, the number 413 doesn't hold any significance to either of them, she just woke up one day and decided it was their anniversary.
Natsu lacks any sense of normalcy, frequently accuses the Only Sane Man of being the weird one, and for a typical example of how his imagination works, his idea of Sagittarius is a combo of Nakajima from Rave Master and a squid.
FLCL's Mamimi, who among many Cloudcuckooland moments, mistakes a television-headed robot for an angelic deity from her favorite video game, and continues to treat him as such throughout the series. It's implied that her cloudcuckoo perspective is a deliberate front, and that she eventually gets better.
Haruka Nanase in Free! spends most of his free time in his bathtub and will strip to his swimsuit if he sees a body of water, including fish tanks.
Hatsuharu Sohma from Fruits Basket will say some of the most nonsensical things.
The teacher didn't like my hair, so now I have to get my ears pierced.
Hohenheim from Fullmetal Alchemist has a way of looking and acting as if he came straight from another planet. A scene in the manga even shows him mumbling to himself while Ed yells insults and accusations at him at Trisha's grave, comparing Ed to "a little boy who has wet his bed and hidden the sheets" in a fairly threatening way. This might partly be a case of Obfuscating Stupidity though, as when he does get serious, he reveals that he's understood the situation way earlier and better than anybody else. Plus, some of his apparent non-sequiturs actually contain important hidden messages and information. Still, everybody notices how ''weird'', socially awkward and absent-minded he is.
A scene in which he talks with Winry at Trisha's grave (and shocks her when he tells her non-ironically that "It's sad" that her parents were killed during the Ishbalan genocide) suggests that he has spent several entire days and nights in the graveyard.
In the manga, Al is disturbed by Hohenheim's body language and way of making terrifying or ridiculous confidences with an impenetrable face and Scary Shiny Glasses—and Al himself is practically a suit of armor.
In a key scene of the manga, "Father", the homunculi's boss, starts acting like a caricature of Hohenheim, complete with non sequiturs, creepy staring, senile mumbling, suddenly standing uncomfortably close to people, and pensive beard-twisting. Ed proceeds to yell at him, "LISTEN TO ME, ALIEN!" An official Yonkoma even shows him letting Ed persuade him to get a 200-years subscription to a Central City newspaper. In the last panel, Bradley/Wrath calls him a "naive Hikikomori with no knowledge of the world."
The central reason as to why he is a cuckoolander is revealed to be spending the last 450+ years getting to know all 500,000+ souls in his head on a first name basis. Hohenheim really does have a "world" in his head to be lost in.
Ed in the movie appears to be one to the people around him. He has good reasons for his bizarre non sequiturs and erratic behavior as he came from another Earth in a parallel universe where the laws of physics work differently and already had numerous psychological issues beforehand, but one can't help but think the people he interacts with must consider him a little bit crazy. At one point, during a pitched battle, he even suddenly moves uncomfortably close to Scar and politely asks him a question.
In Full Metal Panic!, a more disturbing example is Gates. Most of the things he says don't really make sense, and the people who employ him have a hard time understanding what in the world he's talking about. In fact, the last thing he does when Sousuke obliterates his AS (and kills him) is to play with his hair and say, "Maybe I cut it too short?"
That was a call-back to a comment several episodes earlier—when his AS shrugs off an attack by the enemy he declares, mockingly "That might have hurt me, if my sideburns had been shorter!" But Gates really is disturbed—he watches a nature film on squirrels while naked for recreation in one episode. It started out with footage of kittens, and while he was on the phone with one of his subordinates he was furiously tearing tissues out of a tissue box.
Sousuke: "Chidori seems to be bothered by something. Either that or she's been abusing drugs." Kyoko: "Er... I don't know about that..."
Mao references this. When Kaname commented that she thought everyone in Mithril had the same personality and attitude as Sousuke, Mao replied: "Ha ha ha... that kid's... a little special." And other times, she and Kurz reference how Sousuke isn't quite all there. Though Sousuke is one of the few, if not only Mithril member who was a Child Soldier. Sousuke's been fighting in wars since he was eight (and before that, he was being trained as an assassin by the KGB), whereas most of his fellow mercenaries started out when they were already responsible adults; with that kind of upbringing, he probably simply doesn't know how to respond to anything without breaking out some serious weaponry. Makes it a lot less funny when you realize his behavior stems from the fact that he simply can't believe that there are places on Earth where people are not always trying to kill each other. And we have the Student Council President who deems Sousuke's actions... appropriate. No wonder they share mutual respect.
Miki "Nodamiki" Noda from GA Geijutsuka Art Design Class is living in her own little world compared to her friends. She believes that she can remove mold from paint with her "aura" and has started impromptu mini theaters on at least two occasions (once with a collage, once with a can of paint). She is quite boy crazy to boot, to the point of believing random guys have a crush on her. Still, she seems to be on top of things. The manga manages to deconstruct this on a Dream Sequence where the main cast finds out that the supplies on a lost-and-found box have reality breaking powers, with her using it inappropriately.
Dolce in Geneshaft is also a genius, this time in computer programming. She keeps a calm and quiet appearance herself, but communicates loudly and obnoxiously through her puppet.
"Astronomy would be good for me. People are always saying I've got my head in the clouds... though I never remember what I see there."
Katsura from Gintama is apparently quite skilled in avoiding the authorities while carrying out his anti-government activities. Yet, he also seriously thought Gintoki was capable of hiding in a small metal can, and at one point, dressed up as a "yellow curry ninja" in order to rescue his equally bizarre friend, Elizabeth. Any time Katsura makes an appearance, bizarre behavior is sure follow.
Ryou of Gourmet Girl Graffiti has these tendencies from time to time for things unrelated to cooking. This seems to be an inherited trait; her mother once mailed JapaneseRamen to Ryou just because the former saw in their local store the same stuff sold in Japan.
When asked to sketch a bale of rice, bamboo shoots and carrots in Chapter 4/ Episode 3, she drew a bowl of Takeneko Gohan, a dish that can be made from these ingredients.
Fails a test because she studied the wrong subject.
Barely passes the make-up exam for the above, because she fell asleep during the test.
The just-barely-literate Ryuichi Sakuma from Gravitation, and to a lesser extent Shuichi Shindou. They both combine this with Genius Ditz, which is probably the only reason anyone puts up with their glomps, shrieking, emotional extremes, bizarre ideas, and sheer mind-blowing stupidity.
Hikari from Haibane Renmei, who once used the halo mold for making donuts...which resulted in Rakka's halo being charged with static electricity for the first few days after she got it. Rakka was not exactly pleased.
The titular character, who rants about dumping all her previous boyfriends because they weren't aliens, time travelers, or espers, seems to fit this trope at first... until her criteria turn out to be less farfetched than they seem....
She may still qualify, though, as she never realizes she's attending Uncanny Valley High. Even without the reality warping powers, she still does some pretty odd things — believing that wearing a Playboy Bunny suit at school to advertise her new club is a-okay, among other things.
Downplayed because, despite her outward wackiness, Itsuki Koizumi points out that Haruhi is a rational person who ultimately does not believe in the supernatural.
Kuyou Suou. She is an interface for the Sky Canopy Domain, an alien entity with thought processes fundamentally different from those of humans. The SCD is just beginning to learn how to communicate with humans resulting in strange behavior and statements from Kuyou.
Also downplayed for Yuki. Kyon thinks she must be this at first when she dumps a lengthy dissertation on him explaining how she's a fragment of an alien superbrain and Haruhi is some kind of human data bomb; but, of course, it's all true. But she also does some pretty bizarre things later on, like when Kyon tells her to "stop" and she freezes in place until he realizes he has to tell her she can move again.
Saginomiya Isumi has really impressive command over the non-sequitur and is generally completely spaced out, leading to such scenes as her asking a construction worker if the subway involved getting dinosaurs into bullet trains. As a result, Isumi's the only one capable of following Nagi's utterly nonsensical attempts at creating manga.
Isumi's mother and grandmother. As an example, in her introductory scene, her mother couldn't remember which button to push on the intercom to the front gate of her own house, despite the fact that there was only one button.
That's not the worst of it. Isumi's mother is thought by her own mother (Isumi's grandmother) to be the Sanzenin family's new butler. And then once grandmother realizes who she's talking to, she wonders where the butler went. And Hayate is standing off to the side during this entire encounter.
Several of the characters in Heat Guy J could fall into this category, though its most prominent example is the werewolf Boma. The crazy things he does include inserting "Usagi/My bunny" randomly into conversation and randomly appearing and disappearing mid-fight. There are even times where he shows up to a battle—only to sit out the entire time (which the people involved may or may not have told him to do). Interestingly, Clair Leonelli, who is legitimately, frighteningly insane, is not a Cloudcuckoolander at all.
Shinobu Morita from Honey and Clover, who also has the tendency to disappear for days in a row.
Well, that is for work. He still qualifies, especially in the way he treats Hagumi.
While most of the characters are weirdos at some point in this series, Noelle from I'm Gonna Be an Angel! still stands out the most. So much that in the last episodes she manages to come off as one of the saner characters.
Guido Mista is one of the stranger members of Team Bucciarati, a lot of which stems from his Tetraphobia.
Ghiaccio, combine this with his Hair-Trigger Temper, and the rants he goes on tend to end up getting pretty strange.
Vinegar Doppio at first seems like a normal guy, but whenever Diavolo attempts to call him, he suddenly falls into a trace where he does nothing but imitate the sound of a ringing phone. And that's not even getting into the things he'll end up using as a phone.
Andy Doumyouji from K. It's not obvious in the anime due to him being a Bit Character, but rather in the manga Days of Blue where he is a 19-year-old Manchild. When asked to describe his boss, the Blue King, this is his reply:
Andy: Whoosh! Ping ping! Pow pow! That's what his head's like!
Yui from K-On! — She's very very easily distracted. Also, each time she focuses on something new, she can literally forget almost everything else: when she was forced to study for a makeup test she temporarily forgot how to play the guitar afterwards.
Kaizo from Katteni Kaizolives this trope, the first thing we ever see him doing is accusing old people of being aliens and trying to take over earth. Although some of his wild imaginings turn out to be correct.
Sanageyama: This chick is either really brave or really stupid.
Murasakibara from Kuroko's Basketball fits this trope to a T. His appearance alone, would make him an oddball, seeing how he's described as being impossibly tall, with extremely long arms and legs to top it off. The fact that he behaves as a huge manchild doesn't help. It is almost impossible to understand what's going through his head, nor can you guess his motives. Most of the time he just talks in this very slow, almost slurred speech about random topics, usually food. His movements are lumpish and he seems to show interest in very little things and people. Not even in basketball. When Kuroko was asked what Murasakibara was like, the latter responded by saying the guy had a few screws loose.
Kuroko: Whenever he is not playing basketball, he's basically just a kid with some screws loose... Sometimes you meet people like him. A genius in one area, yet totally incapable in anything else.
Love, Chunibyo & Other Delusions: Rikka and Sanae, through and through; even their speech were passed through the filters of their teenage delusions. Yuuta and Shinka used to be, but mostly grew out of it, and is still trying.
Sora and Hajime in Magikano come off as completely nuts, but they may be the only ones who have any idea that something really strange is going on: that everyone is caught in a time loop, living the same year over and over again, and can't escape.
Yotsuya from Maison Ikkoku continuously annoys the main male protagonist with his outlandish behavior, including but not limited to extortion, theft and housebreaking. He is very polite about it, though.
Martian Successor Nadesico: Izumi, one of the Nadesico's Aestivalis pilots, is notable for her bad poetry and her even worse puns (though she laughs uncontrollably at them), and often seems to be off in a world of her own. This doesn't stop her from being a competent pilot.
Takes a turn for the tragic when it's discovered that Izumi had not one, but TWO boyfriends die on her. No wonder she's so loopy.
Minami-ke's Hosaka is so caught up in his own little world he ends up acting his fantasies out in real life. People tend to think he's off his rocker as a result. Further, being a master of the Imagine Spot, we the viewers tend to actually see what's going through his head at the time.
In her first few appearances, Lacus Clyne Mobile Suit Gundam SEED was one. She seemed utterly unaware of the fact that she was on an enemy warship, and condemns Kira to an Accidental Pervert moment when he takes off her dress right in front of him. Gradually, she shifts and shows that she wasn't nearly as dumb as she looked, or really even dumb at all, and often appears very jaded (her father getting murdered by a paranoid nut probably contributed to that).
Both Yokoi and Seki himself from My Neighbor Seki are both examples of that: Seki from Yokois perspective as she notices his constantly playing games she doesnt understand instead of paying attention in class, and Yokoi from the rest of the classs point of view since theres no other way to explain her weird behaviour as she tries to cover for Seki.
The entire security team from Mysterious Joker had this bad in their initial appearance. They got better. Policewoman Momo seems to have shades of this.
Killer Bee in Naruto Shippuden. Let's put it this way: If you have an extremely powerful demonic entity inside of you, and it is significantly more rational and sane than you are, you qualify for this trope.
Naruto himself has been known to be one as well, as illustrated when he showed no problem trying to destroy a wall with a Rasengan while on a stealth mission and was confused on why he shouldn't do it. He also has a tendency to go on about ramen at times when it has absolutely nothing to do with the subject. He was also shown to get distracted easily during his training for the Rasen-shuriken.
Filler character Yuukimaru seems to be one of these. He appears rambling about flowers while Sasuke simply stares.
Although not a Cloudcuckoolander at all, Shikamaru had a couple of scenes. First when he, in the midst of his Chuunin exam battle against Temari, sits down and stays looking at the clouds while he thinks he would like to be as free as them. Not much later, he got surrounded by Sound Ninjas during the invasion and the only thing he is capable to do is thinking about what did he want to do with his life.
Omoi is a borderline case, in that he's not completely out of it, but his minds tends to wander of into insane tangents like how doing too much paperwork can lead him to getting killed in battle or throwing a rock could destroy a village.
Combine a hefty helping of this with a Stoic SpectaclesBishounen and you get Kairi from Nightmare Inspector. He's the owner of a building called the "Delirium," a literal Cloudcuckooland — getting locked in a room there means you get to live all your wildest fantasies until you die (or until you realize that it's just a hyped-up daydream, whichever comes first). Kairi himself is always sitting behind the desk, staring off into space, and daydreaming about all manner of weird things. The reader actually gets to see some of his trips to Cloudcuckooland...
Noda Megumi "Nodame" from Nodame Cantabile, who is a brilliant pianist, but often has strange notions about things.
Gedatsu in One Piece is a villainous example; he often forgets that his mouth needs to be open to talk, or to unreverse his eyes to see, and apparently isn't even able to cross his arms properly without advice. He kills his own Mooks by accident. The main character who faces him doesn't get it and finds his behavior utterly terrifying, though.
Monkey D. Luffy. He seems incapable of giving his actions a second thought (and rarely gives his actions a FIRST thought), and seems intent on asking every non-human being he meets (Brook, mermaids) if they poop, and generally forces the rest of his crew to follow him on his 'adventures' to act as Cloudcuckoolander's Minders so he doesn't do something stupid (they rarely succeed).
Kizaru from the same series counts — he mistakes his wiretap for a phone, as well as asking enemies where his subordinate is.
Not to forget Vice Admiral Vergo, who forgets that he has half a hamburger stuck to his cheek, and before going to battle, asks if anyone has seen his sword - before getting reminded that he is not a swordsman. And when he accepts the corrections of his mistakes, he'll reply in his usual deadpan tone.
Vergo is an odd example. If he weren't so absentminded, he could easily be The Stoic. He has a no-nonsense, imposing demeanor and performs his duties with great efficiency. Nothing about this guy says "quirky" at first glance, but then, he'll walk around with french fries or even a spoon stuck to his cheek without even noticing. And after he's defeated by Law, the latter non-lethally cuts Vergo's body into pieces and sticks said pieces on rails. Completely defenseless, what's the first thing that comes to mind despite his situation?
Vergo: "How will I eat breakfast tomorrow?"
Then there's Baby 5, who accepts requests far too easily because she is "needed." This includes borrowing (culminating into a hundred million beri debt) and marriage proposals, in which her eight fiances have ended up dead with their residing island burned to the ground because of Doflamingo's protectiveness. She immediately tries to kill him in revenge, and then accepts a mission from him.
Let's not forget Kumadori's kabuki theatrics even in the most serious situations, Zeo having so much pride that he can't admit something that isn't in his favor (even though it's so blatantly true), and Fukuro will tell you "my lips are sealed" and claims that he won't reveal information about a specific subject. Immediately after, he'll spill everything on said subject! After realizing his mistake, he claims that he gave it away willingly. It's easier to list the characters that aren't Cuckoolanders in the world of One Piece.
For example, she once cut a conversation with Miyako short by rocketing into the stratosphere. When Miyako caught up with her again and mentioned it, she went "What are you talking about?"
Himeko also seems particularly unconcerned with anything remotely approaching reality, though in a much more energetic way than Ichijou.
Yuu Narukami (Protagonist) of Persona 4: The Animation is shaping up to be quite the Cloudcuckoolander. While Yosuke and Chie are freaking out over things like being inside a TV, a bear mascot talking to them, said bear mascot being hollow inside, and Yosuke needing the bathroom, he's completely deadpan. When bitten by Teddie, he says that it's making him cry in a completely deadpan voice.
Nene Mori of Princess Nine always dreamed of being the manager (gofer/janitor, not coach) of a high school baseball team, just like in all the manga she read. Since she was sent to a private all-girls school, this just wasn't going to happen. Once a girls' baseball team is formed, Nene sees it as her destiny. Unfortunately, while she is very smart, she only knows what a manager does, not how to do it (her family's filthy rich, she's never even done laundry), so she mostly exists to Hang A Lampshade on the more obvious cliches the writers embrace, by suggesting them. Fortunately, she has a good heart, and a butler (and access to lots of resources).
Several characters from Ranma ½ have tendencies this way, notably the Kunos.
One of the biggest is figure skater Azusa Shiratori; she's a teenage girl who acts like a five year old, and will steal anything she considers cute and will give it a pet name - often a fancy sounding female name even if the person or animal she takes is a male. She will also take strange things like cooked fish, rice balls, bicycles, police sirens, and steel girders and give them names.
Elie from Rave Master. As a child, she told her father she wanted to grow up to be a bug. Perhaps because that is impossible, she settles for being the greatest dancer in all the land. To avoid spoilers, let's just say there's a long and very complicated story hidden in all this.
Rebuild of Evangelion: Mari Illustrious Makinami is an excellent example of this trope - when not fighting, that is. Inside an Eva however, she's Ax-Crazy incarnate.
You'd think Usagi of Sailor Moon is a clear candidate, but the Cloudcuckoolander, at least in the anime, is definitely Minako with her infamous malapropisms.
Minako:Mi o sutete koso, ukabu setomono mo are! (Along with throwing your life away, you throw away floating pottery.)
The real quote is "Mi o sutete koso, ukabu se mo are!" (Along with throwing your life away, you may get your chance to survive.)
Kaoruko Odagiri from Saitama Chainsaw Shoujo. Upon seeing the results of Fumio's heartbreak driven chainsaw massacre in the school hallway, she gives her friend a stern lecture... about how she should really be more careful, since blood can be so hard to wash out of your hair.
Emperor Fred from Samurai Pizza Cats, the eccentric ruler of Little Tokyo who largely communicates by saying his name ("Fuh-red!") and scat-singing ("Doo-wah!"). In one episode he caught a bad cold, and instead of becoming delirious with fever, he became sane with fever:
Princess Violet: "He's speaking aloud back there, as if he had a mind of his own!" Al Dente: "Oh no, then he's very sick!"
Umino Mokuzu from Satou Kashi no Dangan wa Uchinukenai (A Lollipop or a Bullet), who claims to (among other things:) Be a mermaid who has been granted human form, need the true friendship of the protagonist or she will turn into sea-foam in one month's time, and to have been sent by her father to buy a machete so that he could chop up a body in his bath-tub. Throughout the early part of the series, it is a major question for the protagonist of the series as to whether or not anything Umino says is true. The part about the corpse was true. Her dad beat their dog and accidentally killed him, so he dismembered him and buried him in the mountains. It's also implied Umino's odd personality is related to her being abused by her father. She also may be subverting this trope as she doesn't seem to honestly believe she is a mermaid and is just either speaking in metaphors or is speaking nonsense.
Fuura Kafuka from Sayonara, Zetsubou-Sensei combines this trope with being a big-time pollyanna to incredibly creepy extents; for example, she believes that nobody could ever want to hang themselves, and those who do are simply trying to "make themselves taller". She then cheerfully goes on to describe how her father went and tried to make himself taller... Repeatedly. No-one is sure if she's deeply disturbed, in heavy denial, or both.
Her forced cheerfulness extends to every aspect of life, even inanimate objects. When she sees a garbage can, for example, she refuses to accept that something as unpleasant as garbage could possibly exist. Thus, she decides that a garbage can is actually "a treasure chest for the homeless."
Taro Maria Sekiutsu can be considered one too, especially considering she comes from a country where apparently massacres happen regularly. She's upbeat, cheerful, and makes little to no sense usually. Unsurprisingly, she gets along great with Kafuka.
Oora Kanako walked into a newly thrashed, blood sprayed classroom, sat down by her desk, which their homeroom teacher, the victim of the recent assault, was lying on nonetheless, and then stared off into the distant nothingness with a vacant smile on her face... The next episode, she's still sitting like that and her classmates comment on that she's been sitting like that for a whole week.
Masaru Hananakajima from Sexy Commando Gaiden definitely qualifies; he practices a martial art based on the idea that confused, unsettled enemies cannot defend themselves. His usual technique to produce that state involves groaning "Ahhhhh" while reaching to unzip his pants.
Angol Mois, a.k.a. the Lord of Terror, from Sgt. Frog has more than her fair share of spacey moments.
Carina Verritti of Shukufuku no Campanella, every time she fantasizes romancing, or being romanced by, protagonist Leicester Maycraft. Interesting that he usually just lets her enjoy herself over it.
Ryou and Fuu from Sketchbook are always together, seemingly living in their own world which only slightly touches upon reality. They do appear to understand each other perfectly though, which is already the case in the manga and which gets exaggerated in the anime so they seem to have some sort of two-person hive mind. They love to play pranks on the other students and often function as some sort of off-beat narrators to the show's events. Still, they will help out their friends in times of need — albeit in their own fashion.
In fact, a lot of the characters could qualify — starting with Sora. Just ask her little brother...
Turning her exam papers into a freakin' GIRAFFE and then freaking out and breaking its neck as she goes pro wrestler on it. Nothing else needs to be said. The Giraffe was still worth 2 points, though.
Excalibur certainly qualifies, what with his rambling, completely disjointed stories and propensity to break into song for no reason. That he is the most powerful weapon in existence, yet cannot find anyone willing to put up with him, is a testament to just how out there he is. You'd probably be this way, too, if you were really an Anthropomorphic Personification of madness. Might also explain why Shinigami and his "Kid" are not all there, either.
Okabe Rintaro, the protagonist of Steins;Gate, likes talking to himself on the phone, rambling about weird conspiracies, pretending to be a Mad Scientist despite barely being able to create random, useless junk... he even calls himself Hououin Kyouma, as it's a much more impressive name than his actual one. He was right all the time--or at least most of it, and he even calls his future self out for not having changed in 15 years.
Miu Matsuoka from Strawberry Marshmallow. She frequently enters the Itou house through Chika's window, yelling one thing or another; remembers a day is Nobue's birthday through stream-of-consciousness; claimed that Santa doesn't bring her presents because she kept asking for things like traffic lights, forcing him to hand off the duty of giving her gifts to her parents; and so on.
Nobue: "I've known her all these years, but I still have no idea how her mind works."
Shiro from Tekkonkinkreet has a tendency to lapse into daydreams or delusions at random. He also tends to use nonsensical metaphors and gibberish in his regular speech.
Mihoshi from the various Tenchi Muyo! series seems like a complete airhead, but manages to save the day on several occasions. This is usually the result of her outrageous luck, but it's also indicated that Mihoshi is much smarter than she seems... at least in the OVA continuity. And while she can be incredibly observant, Mihoshi doesn't always consciously realize what she's observed.
Nia Teppelin from Tengen Toppa Gurren Lagann; at first due to her sheltered up-bringing, but it's quite clear she isn't all there in the head when, even after 7 years in the outside world, she still surprises everyone with her quirky misunderstandings. Simon even remarks that he has a hard time understanding what she says.
Bu-Ling from Tokyo Mew Mew is... strange. She once suggested that Zakuro was going to America to play baseball, and on another occasion thought that spinning plates wile balancing on a ball was a form of ballet.
Minori "Minorin" Kushieda of Toradora! probably counts. In one of her very first scenes she's staring up at the sky and suddenly remarks "The sun is dry...". Her Cloudcuckoolander nature continues from there, but ends abruptly once Taiga's father reappears.
Milly Thompson from Trigun is an almost stereotypical example. She once nearly threatened a shopkeeper with her Hand Cannon when in search of pudding... and got it. Only to drop her grocery bags a few moments later to emphasize a point mid conversation.
Abel Nightroad of Trinity Blood has elements of this, particularily in the manga. It's espicially more prevalent in the earlier chapters, when he's traveling to the Vatican with heroine Esther and Terminator 2-esque Tres; at one point, he opens a window in a moving train because he wants to feel the breeze. A few chapters later, while on a cruise ship, he's immediately suspicious of how nice it is and insists that something bad will happen, citing the events of fiction such as Treasure Island and Titanic, which Esther immediately Lampshades. In this case, he's right, which may qualifies him as being somewhat Genre Savvy.
Dita from Vandread is the resident Cloudcuckoolander for the show. Despite having deep feelings for the main character Hibiki, she seems to forget his name, calling him Mr. Alien instead.
Its more like she's just fond of calling him Mr. Alien, its his nickname for him.
Subverted in Watashitachi No Tamura Kun. Matsuzawa doesn't actually believe what she says, her belief that she is an alien from the moon is an admitted coping mechanism for the deaths of her family members, as she believes she will be able to meet up with them on the moon in the afterlife.
Being a keen believer in the supernatural, Itou has many spacy moments, like when she and Yamada visited the "sealed" classroom, and she blamed anything she saw on a ghost she was sure resided there.
Tsubaki isn't exactly normal either; the guy's standard way of comforting himself is frying tempura, and it actually works because "it's Japanese". The fact that he fell in love with Shiraishi just because she gave him a rude answer to a question also suggests that he isn't quite right in the head.
Himekawa's eccentricities are lampshaded by the narration and in-universe - she has weird priorities (getting Yamada help even though he was barely injured), can be very absent-minded and fails to notice absurd things.
Arisugawa is usually good for a weird idea or a silly comment.
Katsuya Jounouchi/Joey Wheeler of Yu-Gi-Oh! is yet another shonen Big Eater of a space case, prone to many bouts of goofy behavior and painfully awkward moments. He's just, ahem, lucky that he's also street smart, a decent out-of-the-box thinker, and...oh, yes, The Lancer. He may not be able to beat Yugi or Kaiba, but nobody else has ever beaten him more than once.
Ryou Bakura is this as well when his evil side isn't trying to take over, particularly in the manga.
Many of the fodder villains in Zatch Bell! fall under this trope. Victoream will drop everything for a melon, and usually sing a song about it afterwards. Koral Q will drop everything if you missed his awesome transformation, and usually sing a song about it afterwards. Kiees will drop everything if you ignore his brilliant Beethoven mishmash, and... well you get the idea.
Gash also acts this way in the better half of the first season, especially when he's unaware of his powers. (He loses consciousness when Kiyomaro reads spells and at first thinks lightning came from the sky when he uses them.)
Suzume. The fact that she easily forgets what she is doing if she gets distracted by one little thing and that she thinks that Umagon is a sheep while he actually resembles a small horse are just ones of the many traits that classify her as an authentic Cloud Cuckoo Lander.
Though, to be fair, the sound Umagon makes is meant to be the Japanese onomatopoeia of a sheep's bleating.
It's practically required to break into song and dance while fighting in this series. The first probably being Parco Folgore and his partner Kanchome. Their first act onscreen is to duct tape Kiyo to his ceiling and have Kanchome (unconvincingly) impersonate him to fool Zatch (which somehow works). Then upon learning that they're going to be fighting, Folgore breaks the entire situation into a musical production of his Italian pop songs. Kiyo broke into this by believing that Folgore's dance was somehow magically hypnotizing Zatch.
Nanami Kiryuu from Revolutionary Girl Utena. Among other things she parades around wearing a cowbell as fashion accessory and later starts acting like a cow, thinks she laid an egg that she tries to nurture and raise as a child, and becomes convinced that her brother is trying to kill her. Most of the cast thinks she's crazy.