Anna (after she returned to normal) is another example, being unable to solve basic mathematical problems.
Joshua Lundgren in GUN×SWORD straddles the line between ditz and Cloudcuckoolander. He once looked for Wendy by heading into every women's restroom in a train station, not understanding why the women were screaming until he got arrested for it.
The characters of Cromartie High School tend to pass the Idiot Ball around quite a bit, but Hayashida is particularly stupid. The Other Wiki describes him as "dumber than a gorilla"—which, considering a gorilla is actually part of the cast, is proven true in the show. In his defense, the gorilla is the smartest member of the class. Yeah. It's that kind of series.
Himeko from Pani Poni Dash!. She's so dumb, she faints upon SEEING English letters, since her brain can't take it.
Put to shame by Naga the Serpent, Lina's (self-proclaimed) greatest rival. In Naga's defense, Word of God implies she is mentally traumatized, so it's less that she's stupid and more that she's genuinely mentally unwell. Although it's probably fair to say she wasn't exactly very sensible to begin with, given the strong hints she's related to Amelia and Prince Philionel, who are... definitely rather flaky.
Minori from Toradora!, described by one erudite forum member as "a 1-inch deep ball of happy idiot". She's much, much more intelligent than she appears. She's quite possibly the smartest character in the anime.
Italy from Axis Powers Hetalia; the name of the series is even a portmanteau of the Japanese words for "hopeless" and "Italy". America is more of the 'lovable/obnoxious oaf' kind.
Touta Matsuda from Death Note. Most of the time, anyway. In his defense, he is not so much a could-not-function-in-normal-society Ditz. Most of the time, he acts like a fairly normal (if somewhat impulsive and over-enthusiastic) young man. It's just that in a situation where one false move (like revealing your face to the wrong person) could mean instant death, any false move starts to come off as Too Dumb to Live. It also doesn't help that he's working with (or, as it turns out in one case, against) people like Light, L, Near, and Mello.
Sidoh, the Shinigami, is a particularly sweet example.
Rino Rando from Best Student Council. Most of the smarts seem to have been given to her snarky hand puppet Pucchan.
Ash, at least initially. He was just plain stupid: "Hey, that Mankey just stole my hat!" *screams and climbs up a tree after it, while the others just stare at him* He's gotten a lot better since then.
The Team Rocket trio seems to have become cursed to this position ever since encountering Ash, but this tapered off after the beginning of the Best Wishes series.
May and Dawn when they first started as trainers - May was a bit less competent because she didn't really want to train Pokemon, which was before the anime introduced Contests. This even passed on her starter Torchic, who Took a Level in Badass and evolved into Combusken in the middle of Hoenn, eliminating this trait.
Misty's Psyduck, in spades.
Kanako from Maria†Holic is marvelously dumb. She flunked nearly all her exams and, when given notes that "even an idiot could understand" by Sachi, she fails to comprehend even that. She's so single-minded in her pursuit of finding girl-love that she's dim in everything else.
Including realizing that liking girls makes her a lesbian.
Luffy from One Piece easily falls into this trope. From recognizing mixed animals by their least dominant feature to chalking up anything beyond his comprehension (i.e. most everything!) as "mystery" things, Luffy is easily the most gullible and air-headed of Shounen heroes.
What's confusing about Luffy is that he is genuinely stupid most of the time, so it's quite hard to notice the situations where he probably is smart, but just acts like a ditz.
There is no doubt that Luffy is stupid, but it is still not clear to what degree. The one half of the time it seems that he really is severely retarded, and the other half of the time he seems not that ditzy, only acting that stupid because he prefers to not think too much about things.
An extremely ditzy Re-Coder shows up in Code:Breaker. When asked how many people she killed, she says "One, two, three... Ten, I guess, because I have ten fingers! But I'm not in a counting mood, so now I'll kill you painfully!" She never lapses into a Slasher Smile but remains cheerful and perky throughout.
Naruto himself fits this in part 1, though it's really more a case of Book Dumb. He outgrows it after the timeskip.
Arguably, the titular character from Yotsuba&! qualifies. Sure, she's five years old, but what kid that age doesn't even know how a swing works? She can also be led by the nose rather easily. Any moderately intelligent five-year-old would eventually figure out that cardbro is simply Miura in a cardboard box, for instance.
Ringo-chan is a straight example; she's not the brightest bulb in town. In High School Boys and Panties it took her an hour to diagnose the reason for a network problem: the wire was never plugged on. Then she unwittingly flaunts her panties to Motoharu, the President and the Vice-President; fortunately for her she doesn't get to see them in the act, much less their horrified reaction.
Kimihito Kurusu and Mamoru Onodera: She's a birdbrain!
Shinobu of Kin-iro Mosaic is hardly bright. One of the earliest strips shown her scoring zero in math, and despite her European Foreign Culture Fetish, she doesn't know much English (and tried to read an English paper!) and may or may not even know that England and France are part of Europe at all!
A particularly extreme example would be minor Eldritch Abomination Avaggdu from Sláine. So terminally stupid that when tricked into biting his hands, he doesn't notice they're his and starts devouring himself until there's literally nothing left.
Wendy Thornball, the aspiring actress roommate of Angel Love from Barbara Slate's Angel Love series.
Kayla in No Hoper, is an example of a ditz too dumb to take a hint and cannot fathom that Light is not in the least bit interested in her:
Cher Horowitz in Clueless... kind of. She's certainly no genius level intellect, and is definitely more than a little naive and 'clueless', but she's savvy enough when she needs to be and has enough wits about her to 'negotiate' her grades with most of her teachers.
Though he turns out to be a bit of a Genius Ditz in Wake Up Ron Burgundy (a bonus 'film' on made of deleted Anchorman scenes)
Virtually every character played by famed comedian Lou Costello of the Abbott and Costello comedy duo. Occasionally he will even lampshade himself, such as when one of his characters in the film Who Done It? turns on a radio and hears "Who's on First?" (one of Abbott and Costello's most famous routines) and immediately turns it off, remarking how stupid the "short, chubby guy" (actually Costello himself) is.
Volatilus, the sweet but not too bright little dispatch dragon from the Temeraire books.
In Buddenbrooks, Tony is impressed by smart people (like Morten Schwarzkopf — a doctor-to-be with whom she falls in love, but can't marry him because of the Grünlich thing), but is neither book smart nor street smart herself, and calls herself "a silly goose" sometimes. Her poor relative Klothilde is even more so.
Mrs Korobochka the widow in Dead Souls, who hesitates selling her "dead souls" and suggests that "you could still need them".
Tawneee (yes, three 'e's), a minor character from Discworld, a pole dancer.
Jack Pumpkinhead from the Land of Oz series is always described as unintelligent. Some of the words used to describe him are "stupid", "dim", "innocent", "simpleton", "not known for his intelligence", etc. He might also have a bit of an Ambiguous Disorder, as he fails to pick up on vocal cues and sometimes takes sentences to mean the opposite of what they mean (he once called a ferryman 'nice' after he refused to let Pumpkinhead cross a river on account of not having any money).
Lina the servant from Astrid Lindgren's Emil. When the village priest asks her who the first humans were, she answers "Thor and Freya". That does not even make sense in Norse Mythology!
David Rain from The Last Dragon Chronicles, mildly, but those pajamas should certainly get him some recognition in this trope. However, he's grown out of it by the time of The Fire Eternal.
Live Action TV
As in the film example above, Gracie Allen's ditz character supported The Burns And Allen Show, although there was a usually a weird sense of logic behind her statements.
Bull is firmly in Genius Ditz territory, as he frequently is thinking about things on an entirely different level than the rest of the characters. In one episode in which the characters took an IQ test, Bull outscored the rest of the main cast significantly.
Joey's ditziness especially shines through in the subject of geography - at various points in the series he has thought that the Netherlands was where Peter Pan lives, described Chandler's "going to Yemen" ruse for getting rid of Janice as clever because "it almost sounds like a real place", and gone to the bank to try changing dollars into "Vermont money".
There's also Rachel's sister Amy, who notably thinks Phoebe's name is Emma. When Phoebe keeps trying to correct her, she doesn't at all get the hint and instead thinks she's making a "funny noise."
J.D. from Scrubs is an interesting case. Despite being a talented and well educated doctor, he's a massive Cloudcuckoolander who can't stop daydreaming and is constantly blurting out Non Sequiturs, stream-of-consciousness, and ridiculously embarrassing remarks. He also delves into extreme ditz-hood when dealing with certain subjects, including sports (he thinks basketballs come "three to a can" and that Arnold Palmer is famous only for inventing a drink), politics (does not know the difference between a senator and a congressman, and knows Dick Cheney only as "the bald assistant president who has all the heart attacks") and geography (mistakes Austria for Australia and New England for New Zealand. He also thinks there is an Old Zealand).
Jake (To JD): "Are you an idiot?" (The same question was repeated by Dr. Kelso in a later episode.)
There's a couple of issues of Young Justice, set in 'Australia', where the artist apparently made the same mistake (there ain't no mountains like that in Sydney, bub!). And The Simpsonslampshaded it.
A beautiful Double Subversion of this trope occurred in the pilot of Golden Palace, a short-lived and otherwise unremarkable spinoff of The Golden Girls. Rose, confronted by a robber at the front desk of the hotel the girls are running, is too ditzy to even realize that she's being robbed. The robber eventually leaves, with nothing, in frustration. The trope is subverted as Rose immediately calls the police, providing a detailed description of the robber, where he's headed, what kind of car he's driving, etc., ending with "Who is this? Oh, just someone who's not quite as dumb as she appears," much to the delight of the audience. The subversion itself is then subverted as we hear Rose's next line into the phone: "Oh, this is four one one?"
It was said she only had enough space in her head for a very limited number of facts at a time. Telling her a new fact would cause her to immediately forget something important.
Unfortunately this was true, and when Al told her an iirelevant fact before the final question of a sports trivia game show she forgot one. Predictable lay this fact was the answer to the grand prize question "Who made 4touchdowns in a single game?"
That token black kid on Hip Hop Harry, affectionately nicknamed "Stupid Scott" by Joel McHale of The Soup. Despite being roughly around the age of 12, he expresses the cognitive skills of a 6-year-old and has to have explained to him (by the smarter Asian girl) things like how to fill up a bathtub or why its not a good idea to feed ice cream and hot dogs to a pet gerbil. The program goes out of its way to make viewer wonder how on earth he manages to cross streets on the way home.
Susan Meyer from Desperate Housewives started out as the Ditz, but it was largely limited to being a horrible cook and having a tendency to trip over things. This has since been Flanderized to the point where she occasionally just seems mentally disabled, such as her being so desperate to get the new neighbors to like her that she kidnapped their dog planning to heroically "find" it later. It...didn't work out very well.
Susan's mother Sophie is far ditzier than her daughter, especially when it comes to men, coming across as an aged Brainless Beauty. Susan's daughter Julie on the other hand is smart and mature. If this family trend continues Julie's daughter might be the next Marilyn vos Savant.
Dean Winchester, from Supernatural, is like this for anything that doesn't relate to hunting, his family or his car. Most of the time it's adorable but sometimes he can come off as an annoying Brainless Beauty.
Dean: What the hell is this?
Sam: ...she gave you her myspace address.
Dean: What's that? Porno?
Mr. Bean, although sometimes he can be quite bright.
Lord Percy Percy was this from the first two seasons of Black Adder; his role is taken by George from seasons 3 and on.
Edmund Blackadder in the first season, but in series 2 he became the Deadpan Snarker he is known as in the 2nd, 3rd, and 4th seasons. Baldrick also fits this to some extent as well as being a well-loved Bumbling Sidekick.
Mr. Shue had to teach her the rest of the alphabet, because she got frustrated with M and N's similarities and quit.
"I don't know how to turn on a computer."
Finn and Puck aren't the brightest bulbs either (Finn's default expression is an open-mouthed blank stare), though they split the difference and are slightly less dumb than Brittany.
In Puck's case, it's sort of implied that he's not really stupid at all, it's just that he usually doesn't put in that much effort. The moments when he does put in effort in things, he usually does just fine. Finn, however, plays this trope straight.
Luke in Modern Family is always tripping, jumping on the trampoline while on a pogo stick, getting his head stuck in the staircase railing...
Canada's Worst Driver has no shortage of the truly clueless. Andrew Younghusband often wonders how in tarnation they get their drivers licenses, and Season 4 was a toss-up between a ditz and a road rager.
Devo's character Booji Boy (portrayed by their singer Mark Mothersbaugh, in a rubber mask). He is supposed to represent someone who has devolved into a manchild, as per the band's theory of devolution.
2D of Gorillaz. The man introduced himself in an interview with "Hi, my name is 2D, and I'm the singer, and I need the toilet ..." Then in Rise of the Ogre he was quoted as saying:
"I never really thought about what I wanted to do after school, though ... I've never really thought about anything, as far as I can remember."
He is, however, implied to have some Hidden Depths, as he is still capable of composing stunning music and saying some surprisingly philosophical things once in a blue moon. 2D may be more of a Genius Ditz or Brilliant, but Lazy, when he's not thick with painkillers.
Maria from WWE is a good example of a ditz, though this was subverted in the "Trial of Eric Bischoff" episode of WWE Raw, by Maria making a particularly more-intelligent-than-usual speech about Bischoff's failings as a general manager. In a later appearance, Bischoff accused Maria of pretending to be "stupid and sweet" in order to win the fans' favor, which, if true, would make this an example of Obfuscating Stupidity.
The German counterpart was Helmut Kohl in Hurra Deutschland.
Bruno from Bullzeye was an extreme example. When his wife Uschi had her head in bandages (after he injured her without noticing), he thought she was one "Herr Sultan". Sequel SeriesEye TV makes him intelligent enough to be a TV salesman, but not a very good one.
Dennis Day portrayed himself this way in The Jack Benny Program. Apparently he didn't even realise he was supposed to cash the paychecks Jack gave him each week.
Danette and Levin may suffer from an unfortunate Racial Hat, but Levin acknowledges Danette as the Ditz, and Danette acknowledges herself as the ditz! Though thankfully, Levin turns out to be a lot smarter than he lets on, so you don't have to suffer his supposed "idiocy" forever.
Danette gets a little better as well, after the seal of her memories (and seemingly other brain functions) is broken.
Cirno in Touhou. In particular, the manual for Phantasmagoria of Flower View has a screenshot with numbers pointing out items of note (i.e. "1. Player Character", "2. Score", etc.); Cirno was labelled "9. Baka".
Since then Cirno has been nicknamed "Nine-ball" or simply "⑨".
Rumia is known for constantly blinding herself with her own darkness powers and knocking into trees while flying.
The same series also has Utsuho Reiuji, also known by the similar Fan Nickname "⑥" (Six-ball).
Lucia in Shadow Hearts Covenant is described by her own teacher Carla as "slow".
Both Lloyd and Colette of Tales of Symphonia both qualify quite well for the title of The Ditz. A great example is a skit conversation between the two and Regal when Colette asks how Lloyd memorized every single Dwarven Vow (of which there are at least 108).
Lloyd: Since I was a child, I memorized one before each meal and was tested on it. And if I couldn't say it, I didn't get to eat.
Colette: Oh, I see.... There must have been Dwarven Vow memory ingredients in the food.
Lloyd: Huh? R...really?
Colette: I wonder if I can memorize all the Dwarven Vows if I eat Dirk's cooking.
Regal: No, Colette, that's not it. Lloyd's desire for food temporarily strengthened his memory.
Colette: Oh... So Dirk's food has powers like an Exsphere to increase people's abilities.
Lloyd: I see!
Regal: ...Why does the topic of conversation go out the window when talking to Colette?
Tenebrae: Am I really that much of a stick in the mud?
Emil: I can't believe he's still thinking about that.
Colette: I honestly don't see any mud on you. But what's wrong with getting mud on you anyway? Everyone gets a little dirty now and again.
Marta: I don't think he meant that sort of mud.
Colette: Well then, what sort of mud did he mean?
Emil: No, listen. There was never any mud to begin with.
Colette: Oh! So was it more of a muck? Or maybe a slime?
Tenebrae: So now I'm slimy?
Colette: I have to say, I prefer mud to slime myself. It's easier to clean.
Tenebrae: Well, it would depend on where the slime came from.
Emil: Yeah, but think about your fur. Slime would stick to it, while mud would just wash off, no problem.
Marta: Someone, anyone, please make it stop!
One of the female cheerleaders in Osu! Tatakae! Ouendan, Aoi Kanda (the pink haired Meganekko), is completely clumsy when it comes to anything outside cheerleading, whether it's failure to make a meal for sale, failure making a pottery, dropping foods on floor (or not chewing it properly), spacing out on class, and the list goes on, see the bottom of the page. And those are only examples from the first game.
Dragon Age II. Merrill is not incapable but she tends to miss things in conversations and dig herself into holes while speaking. A good compilation is here.
Surprisingly, NOT Goofy from Kingdom Hearts. Despite him easily qualifying for this in the comics and TV-shorts/shows, he's pretty smart in KH, except for occasionally confusing similar words.
Several characters in the Ace Attorney series, such as Maya Fey, Ini Miney, Ema Skye, and Trucy Wright. Ini's faking it, though...and that's not all... Also, Regina Berry, who has trouble choosing whether to go out with a person or a puppet!
Sarrie from Star Ocean: The Last Hope is the living, breathing embodiment of this trope. Just how bad is it? She wakes up on a sacrificial alter, in a room with greenish light...and simply says "Good Morning!" She then remembers that "guests" came in through her window, and she was going to serve them tea...
Viki from the Suikoden series, is actually implied to be pretty smart, but suffering from a severe case of time-displacement-induced confusion. Her younger self, who has done less timehopping, is very smart, observant and has a knack for pointing out other people's idiocy - including her own future self's.
All of the characters in the video podcast Tiki Bar TV drift in and out of this. This is largely because the dialog is improvised while the actors are drunk, leading to some bizarre exchanges that drift back and forth between The Fool and Cloudcuckoolander, and generally end up falling around The Ditz.
Caboose gradually degrades from The Ditz in the first series to being completely retarded and almost completely disconnected from reality (at one point, he loads his gun with crayons and forgets how to spell his name).
Donut also qualifies and stays The Ditz the entire time, though ironically he's the only one from either team who ever managed to accomplish their objective (capturing the flag). Sister could also count when she arrives. Both of them share two traits - speaking terribleSpanish, and both of them talk way too damn much.
Rainbow Dash is belligerently dim and illogical. Once, during a motivational speech, she forgot what the opposite of "good" was. In another episode, she mistook a road sign for a clock—and thought she could time travel by changing the "clock".
Sweetie Belle seems to have fried her brain with Sex, Drugs and Rock & Roll. She once forgot Twilight Sparkle's name, twice, in a conversation lasting less than a minute. She doesn't know what cutie marks are—even though they're a central concept of Equestrian society, and even though she joined a club specifically about cutie marks.
T-Rex in Dinosaur Comics is another male example, as well as a giant green dinosaur example. He worries about being racist against taxi drivers, and makes good-natured attempts to use every school of philosophical thought in recorded history to justify the things he does every day (mainly stomping on people and things).
In El Goonish Shive, Elliot's "party girl" alter ego form make him behave this way.
Crystal, the goth assassin. Uncommon in so far that she has neither the good attitude nor the good looks most ditzes have. If she wasn't The Rival of Haley Starshine (which lets her gain a level every time Haley gets one, for the Dungeons & Dragons rules), she'd probably be long dead. Notably when they fought, Crystal attacked her with pickles. Her reasoning was thus: Haley never ate pickles, but pickles are yummy, so the reason she didn't eat them must be that they're deadly to her.
Sonya of Ménage ŕ 3 is largely defined by her comedy stupidity. There are occasional moments which suggest that she has some kind of brain which she just never bothers to use. but that's unproven at best.
Dustin from Spacetrawler is so consistently stupid that the other characters just start doing the opposite of whatever he advises.
Pierrot: Dusty thinks it's a bad idea, it must be sensible.
Andy of Sticky Dilly Buns is completely incapable of picking up social cues or noticing when he's being exploited, and takes the dumbest advice from whoever offers it, to the point of hero-worshipping the very camp gay Dillon as an oracular source of heterosexual dating advice. Quite what he's doing as a prospective boyfriend for the book-smart, nerdy Ruby is unclear. He is cute, admittedly.
Tiffany Thongbiscuit. When she heard from The Vogue (Pronounced "the vagooey") that "Mad Men" was fashionable. She went to school dressed like a literal mad man.
At the Super Hero School Whateley Academy in the Whateley Universe, one example is the minor character Bubble. Someone comments to herself, "She has a bubble all right. Between her ears." Another good example is the egocentric, villainous Solange, who isn't smart enough to be an effective villain. She uses her powers to absorb an ethereal protagonist and steal said character's powers; she gets run through the Humiliation Conga for her efforts.
February from Starship. She takes the fact that she removed her helmet before she was supposed to on an unfamiliar planet as a sign that she's "super ahead of schedule". Bug and Junior have their moments, too.
Tara from Sex House is a parody of this archetype as frequently found in Reality TV. She, along with the rest of the cast, becomes increasingly more intelligent as the series delves further into the horror genre.
Taipu from the BIONICLE online games and shorts. He at one point mentions that a lot of rocks have fallen on his head, which might have something to do with it. Also a Dumb Muscle, at least among the Matoran.
Goku, from Dragon Ball Z Abridged, is this crossed with Idiot Hero. He is never focused on whatever he's doing, he thinks about food all the time, and he stopped fighting because he was getting bored.
Twister Rodriguez from Rocket Power. Subverted in "Twist of Fate", where after being ridiculed for being a fan of a cartoon on safety, Twister ends up using the knowledge he's learned from that show to get his friends out of trouble in the Grand Canyon, showing that (to paraphrase Rose) he's "someone who's not quite as dumb as he appears".
Practically EVERY character of Polish animated show Hip-Hip and Hurra. It goes so far that you could argue that each of the characters represents a different type of stupidity. Heck, some episodes in the second season almost feel like a race between the characters, to see which one is the biggest idiot of them all.
Gir, from Invader Zim, is amazingly ditzy. He often heads into Cloudcuckoolander territory, depending on the local humidity and/or piggy count.
The perfect example of a male ditz is Gonard from Kappa Mikey, who at one point forgets where his hat is. It's on his head. Also, he takes part in the auditions for a new cast member for Show Within a Show "Lily Mu", despite already being a cast member. All this is in the pilot episode. "Cheerful buffoon" is putting it mildly.
Gonard: Dude! Check out my laced gloves! Hey, where'd my shoes go?
Chris Griffin on Family Guy has an intelligence somewhere between that of a sign post and a bag of moldy French fries. Jillian, Brian's ex-girlfriend, is another example. Peter too, Depending on the Writer.
The titular character from Bonkers, but it could be explained away by his being a Toon; he's super emotional, gets all huggy (and kissy) when he's happy, and seems a bit naive when it comes to human matters (especially in the Miranda episodes). On the other hand, he's very knowledgeable about his own kind, and knows just what sort of Toon stunt or prop can save the day.