Stargirl in Stargirl by Jerry Spinelli. Doesn't wear makeup and carries a ukulele around school and serenades strangers in the canteen with music from it on their birthdays. Also decorates her desk each period with a tablecloth and flowers.
Jenny Wren, from Our Mutual Friend, is physically handicapped to and lives in a mixed world of harsh reality and poetic fancy ("Who is this in pain? Who is this in pain?").
In the Philip Jose Farmer short story "The House of Asterion", the freaking Minotaur is made into one. This is somewhat justified as he has spent much of his life alone in the Labyrinth.
In The Trolls there is a woman nicknamed "Mad Maud" from Aunt Sally's stories who lived in a house filled with stuffed animals she supposedly shot herself and routinely goes cougar hunting in the woods surrounding her house. Said cougars were actually squirrels, and her aim is far from accurate.
Greystone Valley includes a wizard who can't read his spellbook, a warrior who can't stand the sight of blood, and a mouse-sized dragon. Somehow, they all manage to come through when they're needed most, though.
Wendy from John C. Wright's War of the Dreaming is similar to Eilonwy—a Genki Girl who believes she forgot how to fly and runs naked in the woods trying to remember, gets sidetracked during a conversation to hunt for elves, and isn't at all surprised when a armored knight-errant climbs through the window in her hospital room.
Jeanne from Charles Baxter's Shadow Play. She invents new words like "zarklike", "corilineal" and "nutomberized", talks to herself, believes she's drifting on an ocean liner, speaks in metaphors, sees angels and so on and so forth. At the same time, she's often wise and loving. She actually understands she's crazy, but seems to choose madness over sanity and prefer living in her own universe. As her son Wyatt said about her, "you couldn't be insane by choice, but she was".
Professor Trelawney, the Divination professor, dramatically and inaccurately predicts the death of one of her students each year. She also refuses to join a table if thirteen people are seated. She's convinced that the first to rise will be the next to die. She does accurately predict that "one of our number will leave us forever" ... which turns out to be Hermione dropping the class.
Dumbledore comes across as incredibly strange in his thought patterns and interests. During the Welcoming Feast in Harry's first year, his opening remarks were "Oddment. Blubber. Tweak." When Harry hesitantly asked a fellow student about the Headmaster, Percy confirmed that he was brilliant, but a little mad. And according to the man himself, when he looks into the Mirror of Erised, which shows you your heart's deepest desire he saw himself holding warm spoken socks. Though, Harry also stated that he was probably lying as it was a very personal question.
The Bursar from Discworld is something of a Cloudcuckoolander. Since the overbearing Mustrum Ridcully took office as Archancellor of Unseen University and the various weird things that happened since then (including the movies-influenced invasion of Things from the Dungeon Dimension in Moving Pictures and the incident with Windle Poons becoming a zombie in Reaper Man), the Bursar's nerves have been worn threadbare, and given him a tendency to do and say odd things under pressure. Thankfully, his skill with numbers remains no matter how detached from reality he gets, and with a steady diet of dried frog pills, he consistently hallucinates that he is sane (just like everyone else...) and is able to function reasonably well. Though he still sometimes thinks he can fly, and him being a wizard, gravity isn't about to say otherwise.
"The Bursar was, as he would probably be the first to admit, not the most mentally stable of people. He would probably be the first to admit that he was a tea-strainer."
Discworld magic-users, as a rule, seem to cultivate a touch of Cloudcuckoolander-ness. One of the minor wizard characters at Unseen University has an office where the furnishings are entirely constructed of piled-up books, while a young witch-in-training from the Tiffany Aching series pins her hair back in a bun with a knife and fork. Apparently, too much power tends to drive witches insane (think of Black Aliss.) Perhaps she is trying to channel her madness into a harmless form? That's what the book says "All witches are odd. It's best to get your oddness sorted out early on."
Carrot Ironfounderson, with his unshakable conviction that people are good at heart, is frequently thought to be one of these by other characters. They'd be absolutely right about that, if he didn't make it work. From about The Fifth Elephant he stops.
Leonard da Quirm, who designs war machines but believes that no ruler in their right mind would have their army use such horrible weapons. The bad news is, Havelock Vetinari is the only ruler in his right mind on the Sto Plains by these standards, realizing that war and empire-building are more trouble than they're worth; the good news is, Vetinari has Leonard safely locked away and working for him.
Moist von Lipwig is prone to employing these, including Stanley the pin collector, who was raised by peas. Not on, by. Also Owlswick Jenkins, an even more off-kilter Genius Ditz forger who makes copies better than the real thing. For that matter, Moist has some moments like this himself, although it's mostly a result of him living on the edge.
The Harpell family of wizards in The Legend of Drizzt books. List of "experiments" include trying to cross a horse with a frog; accidentally turning themselves into dogs; physically relocating their brains to their buttocks; separating their eyes from the rest of the body and getting stuck that way; believing double initials to be important omens, etc., etc. All the while beaming happily. The really weird part is that their experiments tend to have successful side effects — the one who turned himself into a dog, once turned back, ended up a werewolf; the one who tried to cross a frog and a horse succeeded (he dubbed the result "Puddlejumper"); and the brain-switching was actually with purpose, as it was done to fight against brain-eating monsters. This may mean the family hinges on being a clan of The Fool.
As for Harkle Harpell's eyes being teleported away from his body, he actually had an excuse that time: it happened during the Time of Troubles, during which everybody's magic spells went wrong somehow. Harkle tried to teleport his entire body before he knew the situation, the result being that he was able to see his intended destination (since his disembodied eyes were there) and talk to the people there, but his body remained behind. He was blind to his immediate surrounding until his colleagues were able to help him make the trip overland and reinsert the eyes in their sockets.
In Garcia Lorca's The House Of Bernarda Alba, the grandmother appears completely crazy and delusional; she takes out the jewelry and says she wants to get married, then appears cradling a lamb as if it is her baby. Yet she occasionally says what all the other characters should be thinking, and is the first to voice her protest against Bernarda's tyranny.
In Kurt Vonnegut's Cat's Cradle, fictional Nobel laureate Felix Hoenikker, "father of the atomic bomb", was so easily distracted that, at one time, he completely abandoned the development of the atomic bomb to study the skeleton of turtles... his daughter suggested his desperate colleagues to simply remove anything turtle-related from his laboratory, and he'd forget about his fascination with them completely (they did, he did).
Most characters in Alice in Wonderland count, but the Cheshire Cat is arguably the most famous. He's also a recurring character in the Thursday Next series, where he's portrayed as smart enough to manage a library containing every book ever written single-handedly, but still spends most of his time asking bizarre and irrelevant questions.
In Patricia C. Wrede's The Seven Towers, the sorceress Amberglas is somewhere between this and Obfuscating Stupidity; her constant rambling digressions seem to be genuine, but she's much sharper (and more powerful) than she gives the impression of being, and frequently she has important things to say if you can sort them out from the nonsense.
An example that helped define this trope is James Thurber's 1939 short story "The Secret Life of Walter Mitty". The titular hero is a mild, unassuming man who's prone to spinning off into elaborate heroic fantasies at the slightest real-life suggestion.
Animorphs: Tobias is one of those up until the end of the first book. After that his mind is much more 'down to Earth', the irony being that a lot of the time his head is up in the clouds, because he's a bird.
Awareness is like consciousness. Soul is like spirit. But soft is not like hard and weak is not like strong. A mechanic can be both soft and hard, a stewardess can be both weak and strong. This is called philosophy or a world-view.
Holden Caulfield is more Cloudcuckoolander than Emo Teen.
Then there's Seymour Glass: who (must) at least visit Cloudcuckooland...think about it - in "A Perfect Day for Bananafish" — his rant against the woman unfortunate enough to be on the same elevator: "If you want to look at my feet, say so. But don't be a God-damned sneak about it." Usually, though, he's too busy embodying human kindness as his family's own personal reincarnation of the Buddha (and after his suicide, more so).
In Alison McGhee's Falling Boy, everyone is a Cloudcuckoolander to some extent or another. With the Only Sane Man being a 16-year-old going through a major life crisis, the book consistently refers to "(character name) World".
Zarniwoop: And they ask you to make decision for them? About people's lives, about worlds, about economies, about wars, about everything going on out there in the Universe? The Ruler of the Universe: Out where? Zarniwoop: Out there! The Ruler of the Universe: How can you tell there's anything out there? The door's closed.
To the Ruler, everyone else (if they exist) is the Cloudcuckoolanders. They persist in believing things that they have no immediate, direct evidence for — like what's on the other side of that closed door — and insist that things are as they say they are without even considering the possibility that they could be otherwise. And then they get angry about it.
Angela of the Inheritance Cycle comes out with random non sequiturs frequently. In her spare time, she tries to prove that toads don't exist. Even when she's HOLDING ONE. This may lead to a Mind Screw, she and the main characters get into a discussion about how the toad she's holding is actually a frog...excuse me, my brain hurts...
Though, there is the possibility that she is Obfuscating Insanity, as there are a few times where she drops the weirdness. Namely, when she finds out Eragon met her mentor, and when she crosses enemy lines to poison the invading troops.
From P. G. Wodehouse's Blandings Castle novels, Lord Emsworth. Emsworth is a doddering old man who cares about nothing more than his pig (which he christened the Empress of Blandings). Want to talk to Emsworth? Chances are he'll end up rambling about pigs, derail the conversation based on semantics, or just plain space out and not listen to you at all. Even if you're lucky enough to have a lucid conversation with him, ten minutes later he'll have forgotten about it (and quite possibly you) anyway.
Bat Jarvis, from "Psmith, Jouralist", the gangster who's prone to ask you if you've ever had a cat with different-color eyes.
Sacksby Senior from Cocktail Time. He has a habit of misinterpreting everything that is said to him, and he also refers to his acquaintance Lord Ickenham as 'Scriventhorpe', for no discernible reason. Out of Wodehouse's cloudcuckoolander characters, he is arguably the most divorced from reality:
Sacksby: Ah, Scriventhorpe ... you seen Flannery lately?
I'm not absolutely certain of my facts, but I rather fancy it's Shakespeare—or, if not, it's some equally brainy lad—who says that it's always just when a chappie is feeling particularly top-hole, and more than usually braced with things in general that Fate sneaks up behind him with a bit of lead piping.
In fact, let's just go the whole nine yards and say that everyP. G. Wodehouse character probably has at least a smidge of this. Yes, even you, Jeeves.
An interesting variation occurs in Summer of Eternity. The mother of one of the characters learns that her husband helped commit a murder and has been arrested. She has a complete breakdown, as a result. For the rest of the book, she is in a cheerful mood and is off in her own little world, believing that her husband is off at work rather than at prison. The trope is played straight, but due to the context in which it is played, it comes across as heartbreaking rather than funny.
A great deal of the plot of Pippi Longstocking revolves around Pippi living in Cloudcuckooland while the adults and others don't.
Fregley of Diary of a Wimpy Kid. With the things he says to people ("I bet I can fit your whole foot in my mouth!" and "Wanna hear about my hygiene issues?"), the things he does (play in ball pits, show people his secret freckle, chase people with his boogers) and the fact that anything with sugar turns all of these things Up to Eleven, he makes some of the examples of this trope look normal.
In Moira J. Moore's Hero series, being a Cloudcuckoolander is the first symptom children show when they will grow up to be weather-workers called Sources (and be required to have a soulmate The Stoic who can translate for them).
Odiana of the Codex Alera series lives somewhere in the hinterlands between Cloudcuckoolander, The Ophelia, and Ax-Crazy. Not entirely unexpected, since she's an incredibly powerful empath with a past that could have driven even a normal person crazy.
Dr. Roger Burrows, the wanna-be Adventure Archaeologist of the Tunnels series. He tends to get so caught up in his admiration of ancient artifacts that he neglects trivial matters such as the fact he ran out of food three days ago and is surrounded by large carnivores. He does however have enough of The Fool archetype to survive most dangers by virtue of simply not noticing them.
Deconstructed in Ironman with Hudgie. His inane ramblings are treated as a severe threat to his own well being, and it's heavily implied that he is incapable of rational thought anymore. Oh and the reason he's like this is due to the horrific emotional abuse and flatout torture his psychotic father subjected him to his entire life.
Goss from Kraken is an interesting case. He's either this trope or a subversion, depending on your point of view. He does understand what's going on, but has a tendency to speak in such a bizarre vernacular (speaking to people as if they were school friends, or magical princesses, or something equally as strange), frequently chides his silent partner Subby for being a chatterbox, and has a tendency to ignore whatever others say that doesn't fit into his strange little world. Given that he's an Ax-CrazyPsychofor Hire, his bizarre way of behaving is even more terrifying.
Anne Shirley of Anne of Green Gables falls victim to this moderately, especially in the earlier books. She just really loves living her own little fantasy world, a world where everything is really, really romantic. She asks Marilla to call her "Cordelia" rather than Anne upon their first meeting, claiming it sounded better. It's to the point of hilarity, really. She gets herself into all sorts of scrapes as a result of having her head up in the clouds, including sinking her best friend's father's dory while re-enacting Tennyson's "The Lady of Shallot". She mellows out with age, but still retains her wild imagination.
Robert Marsh from Darkness Visible, who was driven mad by the influence of Unreality. The same fate befalls about a third of London's population before the book is done. Not that being insane stops Robbie from contributing to the plot...
Emily Dorothea Seaton, protagonist of a series of mystery novels by Heron Carvic. She's not exactly out of it, but her thought processes are difficult for others to follow. Unlike other amateur sleuths, she has no idea she's involved in mysteries. Oh, and if you mean her harm, stay clear of the brolly....
In the In Death series, Dennis Mira, Dr. Mira's husband. Incredibly sweet and empathetic but rather spacey. Eve finds him oddly charming.
Oblomov. It's not really funny: Instead of caring for the village he owns, he spends years of dreaming up improvements and does effectively nothing.
Gilbert Hays in Of Snail Slime, who spouts Non-Sequiters left and right, and seems to change his personal view of the world at the drop of a hat. Partially because he's a brainless walking human shaped tumor. Somehow. Oddly enough, also an Author Avatar.
In The Last Unicorn, the butterfly sings songs, recites poetry, quotes a warning from a matchbox at one point, and occasionally says something useful. It's at least implied, if not stated outright, that verbatim parroting what he's heard others say before is actually the only way any butterfly can talk at all. He seems to understand what the unicorn is after well enough, though.
Dark Future: Commander Fonvielle in Comeback Tour, who regards the Josephites who've drained and reactivated the flooded and derelict Cape Canveral, as new NASA staff and Roger Duroc as the new President of the United States, while being otherwise entirely competent and connected to reality. Well, apart from a tendency to drool and eat his beard. He's also a literal Space Cadet.
Eliza in Someone Else's War. Her chipper nuttiness is a breath of fresh air, considering that the rest of the novel is one relentless punch to the gut after another. The same novel also gives us Abdel, a quirky little weirdo who arbitrarily decides that he is psychic.
The Pirate Captain from Gideon Defoe's The Pirates! series. In one book he is told to concentrate and stay focused. Somehow he turns this into a ten-page daydream about a world made out of mint, where a lazy king tricks people into doing his yard work.
Dean Moriarty in On the Road. Kerouac's fictionalized version of Neal Cassidy drives 100 mph naked through the midwest in a borrowed car without a second (or first) thought. This not extreme behavior for this guy.
Myrnin (a vampire mad scientist with bunny slippers) and Miranda (a psychic ghost child) in the Morganville Vampires series.
Discussed in Lord Chesterfield's Letters to His Son. He wasn't too fond of this trope: "Sir Isaac Newton, Mr. Locke, and (it may be) five or six more, since the creation of the world, may have had a right to absence, from that intense thought which the things they were investigating required." (letter I)
Lawrence Pritchard Waterhouse, in Neal Stephenson's Cryptonomicon. He fails to realize that the barren place in New Jersey, full of pine trees, is in fact the Pine Barrens of New Jersey (that he's come to see) until it's pointed out to him. In a wondrously hallucinatory sequence set in those very Pine Barrens, he sees "the world's globe, not the globe fleshed with continents and oceans but only its skeleton: a burst of meridians, curving backwards to cage an inner dome of orange flame" surrounded with "webs of cable and harnesses of electrical wiring ... vast, ramified snarls of ropes and piano-wires, cables and wires". Only when he reports this to his friends the next day as a dream of a burning zeppelin do we fully realize that Waterhouse witnessed the destruction of the Hindenberg.
Patty, the 12-year-old protagonist of Summer of My German Soldier, is virtually friendless and suffers abuse at the hands of her parents. She often escapes into daydreams as a coping mechanism.
Apparently how Wiress's traumatization from being in The Hunger Games has manifested. She rarely speaks, and when she does she tends to drop of mid-sentence, she has trouble expressing her thoughts, and she has a habit of "randomly" reciting old nursery rhymes and seemingly random words or phrases. But she is very smart and knows what she's talking about, if you can figure out her train of thought.
Brandon stands out in The Leonard Regime due to his unusual behavior and overall obliviousness.
Faye from The Grimnoir Chronicles is a teleporting Okie girl who thinks several times faster than everyone else and is really good at killing people. She tends to sort everyone she meets into one of three categories: 'Friends,' 'Stupid,' and 'Needs to Die.'