Goku from Dragon Ball. Though it's implied that he had brain damage as a baby due to hitting his head, and not to mention he was almost totally isolated from others until he was 12.
Maron, a filler character, in the Garlic Junior Saga, is this when she insults Chi-Chi and Bulma by calling them old ladies (and you can guess how the former reacts).
Little Marron, Krillin & Android 18's daughter, also qualifies. In a scene in the Great Saiyaman Saga, when Master Roshi asks if he wants to participate in the tournament, she replies with "No way, you're too old!!". For Marron, this is a Justified Trope, as she is only 3 years old and she doesn't know any better.
One Piece: Monkey D. Luffy's ability to do this is legendary. While in the tower of the Shrinking Violet mermaid princess, he starts eating her food while she talks to him. His mouth is filled with food, so his cheeks bulge out. This is new to the innocent girl, so she pokes his cheeks, and he shouts at her for it. She begins to well up with tears, and he calls her a coward, a crybaby, and says in a completely happy, joking manner, "I don't like you one bit!". He obviously thought he was bantering, since the next thing he says is to suggest she sneaks out of the room to go on an adventure, in as happy and joking a manner as before.
Miyako in Hidamari Sketch does this a lot. It's hard to be sure when she's just oblivious and when she actually is winding up Hiro.
An episode of Digimon Adventure was focused on Mimi getting into trouble after she got upset at Izzy, who ignored her in favour of working on his laptop. He had no idea why she was crying, or that he'd been ignoring her at all.
Haru from Tsuritama who tries to cheer up Yuki about his grandmother's hospitalization by telling him that everyone dies at some point. This is because Haru is a possibly immortal alien who struggles with understanding things from the view point of us Puny Earthlings.
Higurashi: When They Cry: Keiichi does a minor variation towards Mion in the Watanagashi arc, by not giving her the doll he won, reasoning that she's too boyish to appreciate it as Rena (who takes home anything she finds cute) would; this instance of his calling out her boyish traits (unlike most other times) deeply hurts her feelings. In the original Visual Novel, Keiichi has to get lectured by both Rena and Shion before he finally realizes what he did.
Masao from Shiki is mostly just a Jerk Ass, but there's many scenes where he comes off this way too.
Setsuna in Mahou Sensei Negima! tends to act far too formally and subserviently towards those she feels have a higher social class than her. For example, she always refers to her love interest as ojou-sama/milady and acts more like a servant than a friend. Konoka, for her part, keeps telling her to quit it to no avail. Near the end of the manga, she actually makes Asuna cry by acting even more subservient towards her than she does towards Konoka after Setsuna learns Asuna is actually a princess. Normally, she's Setsuna's best friend, which makes it quite painful to be treated like that. It was a slight exaggeration of how she really felt, but she wanted to make sure Setsuna cut it out immediately rather than make a habit of it.
Ian in A Cruel God Reigns does this to Jeremy when he actively tries to make their new step-family a happy one. What he doesn't know is that his father is sexually abusing Jeremy every weekend when they come home from their boarding school.
Ian: The plan is to make this a loving household of Lynn Forest, aiming to create a peaceful family.
Jeremy: Will it all...work...out?
Ian: We'll make it work Jeremy! And in the end we'll all be happy.
In Girls und Panzer, when Ami, temporary tankery instructor for Oarai, sees Miho among the assembled students, she points out that Miho's mother (Ami's tankery instructor) has done quite a bit for her, makes a polite inquiry about how Miho's sister is doing, and says the Nishizumi school has a long history. Despite having no ill intentions toward Miho, Ami ends up upsetting Miho by bringing up her family (Miho, unable to adhere to her family's Second Place Is for Losers mentality, had until recently quit tankery), but Saori quickly moves to Change the Uncomfortable Subject.
Saya of Servant × Service tends to speak her mind without even considering the potential consequences. Particularly evident in Episode 6, where she unwittingly sent the normally carefree Yutaka into a Corner of Woe by passively saying that he's beneath her, and a flashback reveals that she rejected a boy's confession by saying he should've looked at himself in a mirror and thought again (she meant she thought he could do better). Eventually Chihaya had to warn her against rejecting Mrs. Tanaka's marriage offer so as not to cause heart attacks.
Nia in Tengen Toppa Gurren Lagann, due to her sheltered upbringing. She is completely oblivious to any negative mood, which doesn't endear her to the others, especially after Kamina had just recently died. She also cheerfully turned down Simon's proposal. Fortunately Kiyoh and Kiyal make her realize her accidental mistake.
Because she lacks social skills, Laura Kinney aka X-23 tends to do this. After an adventure in Limbo, Laura sees no problem with telling Surge (who wasn't present) that her boyfriend Prodigy had his heart ripped out (he got better) when all the other students were evasive about it (even implied that this was why Nori asked her about it after the others didn't come clean). When Laura is later attending Avengers Academy and Wolverine brings some of her former classmates from Xavier's there to keep them safe, she greets Dust by telling her she "smells healthy." After Dust reminds her it's not polite to tell someone how they smell, she innocently says that because she can't see her (Dust practices hijab and covers herself in public) it's the only way she can tell.
Klara Prast of the Runaways once mistook the X-Men for demons, and on another occasion, mistook Tigra for a prostitute. She's also been on the receiving end of innocent insensitivity; Victor and Chase have used the fact that she was once married as an excuse to talk about sex around her, because she presumably already knows about it. It doesn't occur to them that she'd rather not be reminded of that fact...
In Hopes and Follies, Twilight assures Trixie that she doesn't have to worry about their past conflicts, because nopony holds her responsible for it and they hardly even remembered the Ursa incident until she came back. It's not until after Trixie storms off overwhelmingly pissed that Twilight realizes that a professional showpony would want to be remembered, even as a villain. Not to mention that those events were some of the most defining moments of her life. And Trixie has an overwhelming need to be recognized by Twilight, one way or another. This results in Trixie resolving to become an enemy, rival or problem that Twilight can't ignore... ironically, while Twilight's resolving to become closer to Trixie and accept her as a friend.
Film - Animated
Fix-It Felix Jr. of Wreck-It Ralph has this painfully so. He can't bring himself to tell the Nicelanders to let Ralph in his birthday party, he accidentally causes Calhoun to suffer a Heroic BSOD when he calls her "one dynamite gal" and only realizes how crummy he's been when Ralph slings back Felix's accusation that he doesn't know how it feels to be treated as a criminal.
Anna in Frozen is made to forget the fact that her older sister Elsa has ice powers after the latter nearly accidentally kills Anna while playing with them. The fear and guilt force Elsa to isolate herself for over a decade, which Anna does not understand. So naturally she showers Elsa with Armour Piercing Questions, causing her to break down and flee the castle.
Anna: Elsa, please, I can't live like this anymore!
Film - Live-Action
The Purge: The youngest Sandin kid is asking his parents why they don't kill during The Purge. He thinks it's a game and doesn't quite realize yet that it isn't.
In Elf, Buddy meets Miles Finch, a little person. Having grown up with Santa Claus and his elves his whole life, he assumes Miles is an elf and addresses him as one, asking how things are back at Santa's workshop. Miles is enraged, thinking Buddy is doing short jokes. Throughout the whole scene, Buddy doesn't understand his mistake, even after Miles beats him up.
Mr. Spock of Star Trek fame always had a little bit of this going all the way back to the original series, due to his being raised in a society where emotions are suppressed in favor of logic, much to the annoyance of Dr. Mc Coy and the others. Captain/Admiral James T. Kirk was usually more patient with Spock due to their Heterosexual Life-Partners friendship, but in Star Trek IV: The Voyage Home Kirk, after putting up with an even more Innocently Insensitive than usual Spock (who was still coming off of rebirth) in the 20th century finally loses his temper and snaps at Spock who, upon learning that the window of opportunity to snatch up two whales is rapidly closing (thus placing the future of the Earth in dire peril), bluntly states that their mission won't be successful and states it as if they were running a grocery errand. Specifically Kirk tears into Spock with an incredulous "Our mission? Spock you're talking about the end of every life on Earth! You're half human! Haven't you got any God damned feelings about THAT?!"
In X-Men: Days of Future Past, after Mystique escapes the peace conference, she is outed as a mutant on the news. She manages to get to a hospital and get her leg bandaged in her normal human guise. The nurse who is doing it is watching the earlier footage and pities Mystique's appearance, wondering "It must be hard waking up each day and seeing that in a mirror". Ouch.
Hermione Granger comes off like this in Harry Potter at least once a book, arguably downplayed in the movies.
Princess Eilonwy has moments of this in The Chronicles of Prydain series.
Depending on interpretation, Sherlock Holmes. Opinion varies on whether he's genuinely socially inept or deliberately spiteful to people who aren't as smart as him. The 2009 film favours the latter explanation, but critics who stress Holmes' loneliness as a character trait favour the former.
The BBC series Sherlock seems to use a bit of both - he once asks John whether a comment was too insensitive, but also makes fun of everyone for not understanding his deductions. We haven't seen much of the loneliness outright yet, but he sure does get upset when John's in danger.
In the BBC series, he is apparently a Sociopath, as well.
He claims to be one, to be sure, but the fact that he shows genuine concern for another human being pretty clearly tells that if he has a disorder, it's not as serious as he thinks. Or perhaps John is just the exception.
Both presentations may be correct. Individuals with exceptionally high IQs often have difficulty with proper social interactions, usually coming off as either distant, patronizing, or outright arrogant and insulting (even when it is not their intent). Psychologists think it comes from their altered viewpoint of reality. People with high IQs easily make intellectual connections and usually have a better understanding of things. But even when they know intellectually that it is due to their high IQ, they can't always grasp why no one else gets it or may be frustrated by how they need to explain "simple" things. For Sherlock, who likely has a very high IQ, he doesn't get why everyone else can't see the world the way he does. To him, he is pointing out things on the same level of obviousness as "The sky is blue" and then dealing with people who are so dense they need it spelled out to them (even though no one else would ever make those connections).
His mom is this in another way. While Sheldon doesn't always realize that he's being condescending about others' intellect, Mrs. Cooper is the type of Born Again Christian that would be likely to tell someone You Are a Credit to Your Race or use an outdated, racist term (Leonard eventually has to make her list of what she can't say). That said, she's so sweet and comforting (unlike her son) you know she doesn't mean anything by it, it's just a side effect of being born and raised in East Texas.
Rimmer from Red Dwarf is a more obnoxious variant - yes, he's a pain in the neck, but most times he thinks he's genuinely doing the right thing. Even if he does have Manipulative Bastard moments. Cat's a more straightforward example. Actually, you could just shove everyone in this category, they all have their moments.
Mr. Pither from Monty Python's Flying Circus (he's on a cycling tour of North Cornwall). He's a perfectly kindly soul, but oblivious to other people's feelings.
Monk. His Hyper Awareness lets him in on all sorts of details about people, and he's not always clear on which ones are better to keep to himself, such as when he sees the date on a woman's credit card and realizes she's lying about her age, or deduces that the judge at a hearing has been having an affair with his secretary.
Sherlock Holmes has a big moment of this in the second episode of The Adventures of Sherlock Holmes and Doctor Watson, during the scene with Watson's pocket watch. Brilliant as Holmes is, he hadn't anticipated that discussing Watson's ill-fated alcoholic brother might upset him.
Also Sherlock from BBC's Sherlock. He tends to deduce things and think he's being kind by letting the concerned parties know: telling Molly that Jim (her boyfriend) is gay, informing Mrs. Hudson that her love interest is married and a casanova, deducing presents people give him when he's hardly touched the package, etc. He eventually begins to rely on John to give him a heads-up when he's gone too far.
Sherlock:(After asking why a woman would continue being upset about her daughter's stillbirth a decade ago) Ah... Not good? John: Bit not good, yeah.
Star Trek: The Next Generation's Mr. Data, being an android, is often insulting without meaning to be. In Liaisons, he gives Worf advice on dealing with a fractious diplomat who's visiting Enterprise:
Data: I have heard that in moments of diplomatic tension, it is often helpful to find elements of commonality. Worf: Ambassador Byleth is demanding, temperamental, and rude! Data: [sincerely trying to be helpful] You share all of those qualities in abundance! Prehaps you should try to build on your similarities.
Bashir: "I didn't want some cushy job or a research grant; I wanted this - the furthest reaches of the galaxy, one of the most remote outposts available. This is where the adventure is. This is where heroes are made. Right here - in the wilderness."
Kira: "This is my home."
Reid from Criminal Minds sometimes falls into this trap, mostly because his social skills aren't great and, therefore, he tends to forget about them when he gets really excited or is concentrating on something. For example, at one point the team is tracking a killer who has kidnapped a young girl that Morgan is very attached to. Rossi worries that a radio announcement might lead the killer to change vehicles. Reid gets about halfway through brightly saying, "Or he might kill the kid!" before seeing the look on Morgan's face and quickly backtracking.
Castiel from Supernatural is particularly prone to the trope. He called Sam an "abomination" in order to explain a point, and complimented Dean by telling him, "you're not the broken shell of a man that I thought you were."
Michael Scott from The Office. Even when he's trying to be well-intentioned he doesn't realize how much the things he's saying can be rude or potentially offensive.
Dwight Schrute casually and without malice insults people who fall short of his standards of efficiency and skill, which is nearly everyone. His coworkers generally blow it off.
Arthur from Merlin was prone to this in earlier seasons towards the poor. Best demonstrated in The Once and Future Queen, where he's staying with Gwen, a maidservant from the castle. He offers to cook her dinner and then cheats out on it the first chance he gets. She finds out and confronts him about it. This exchange happens.
Arthur: Look, I can kill a chicken from a thousand paces, just don't ask me to cook it. That's what servants are for. Gwen: *Death Glare* Arthur: *realizes what he said* I didn't mean..
Red from Solatorobo. His sister Chocolat is constantly chiding him for not understanding girls' feelings, and Elh calls him "an idiot with a bad mouth" when he continues to stick his foot in there.
Minsc in Baldur's Gate being a brain-damaged warrior with the mind of a child, has a few banters that paint him in this light. Everyone realises his true intentions, and nobody ever gets permanently insulted. Boo is also quick to correct him when he puts his foot in his mouth.
Shizune Hakamichi from Katawa Shoujo can come across as being very blunt to point where she comes across as being flat out bossy. This is in part the result of her being deaf and because of this communicating with others directly is difficult for her along with the fact that she cannot perceive vocal cues of emotion and intent in other people. It does not help the her interpreter Misha seems to have her own troubles reading social cues in other people, leading to more than a few "blind leading the blind situations" including the panic attack incident in Hanako's route.
Hisao himself falls into this at times, especially early on when he's not sure how to talk to people with disabilities. This can be a problem in Hanako and Emi's routes; in the former, he can deeply upset her if he pities her too much, and in the latter, he can anger Emi if he is too aggressive in trying to protect her.
Sakuya Shirogane Le Bel from Hatoful Boyfriend. Classist (to Ryouta and the player character), racist (to Yuuya, Anghel, and the player character), ableist (to Oko San), and a royal Upper-Class Twit, and it takes him most of the game, if the player's on his route, to even acknowledge that these are bad things. However he also has a Freudian Excuse: his father raised him to believe himself above everybirdy else, and Sakuya cannot comprehend that his father could be wrong. In the Bad Boys Love route, finding out that not only was his father wrong but not even his father gives Sakuya a full-blown Heroic BSOD.
In Anghel's route, Sakuya says quite a few racist things about Anghel in the presence of the player character, who echoes them later.
Katherine of Wapsi Square is remarkably observant, but lacks any social skills, so it makes sense that she would fall into this trope at times.
Izor: Something needs to be done about Walter. Marty: Yeah. No fair keeping all the cute ones up on the bridge. All we get is Suehere.
Jake of Homestuck. Most likely due to his upbringing as an orphaned, isolated inhabitant of a deserted jungle island, Jake has a tendency to be oblivious to the feelings of others, mostly Jane's. It's also implied that in his previous incarnation as Grandpa Harley, he was similar and ran away from home and from Nanna without apparently considering how it made her feel.
Hazel of Girls with Slingshots is not good with lesbians, babies (and people who have them), animals, or her boyfriend. (The last gets her dumped.)
Jamie:Why are we friends, again?
Candy's reactions to being called out on her misandry seem to point to her being this way, too... though attempted rape is kind of pushing the definition of "innocent".
My Little Pony: Friendship Is Magic's Pinkie Pie often falls into this trope. In "The Super Speedy Cider Squeezy 6000", she can't stop gushing about how great the cider at Sweet Apple Acres is, despite Rainbow Dash (who didn't get any cider) growing increasingly irritated. What makes it even worse is that Pinkie Pie had also a) gave the suggestion to other ponies to camp out in front of the cider stand, b) was in front of said line and c) put up a pile of coins and walks off with at least ten mugs of the frothy stuff without realizing that others wouldn't get sips. Thankfully she gives one of her mugs to Rainbow Dash at the end.
The episode "A Friend in Deed" is basically twenty minutes of Pinkie Pie annoying Cranky Doodle Donkey while trying to cheer him up.And she unintentionally helped cause the termination of Nightmare Night in "Luna Eclipsed" due to managing to alienate Princess Luna. She genuinely thought it was just part of the fun.
She takes this to the extreme during "Filli Vanilli", constantly setting off Fluttershy's stage fright and upsetting her.
Twilight Sparkle is pretty prone to this herself. In "Baby Cakes", she innocently tells Pinkie that she knew that Pinkie probably couldn't handle the responsibility of caring for baby twins. She doesn't seem to notice that Pinkie is offended by this, even as she is pushed out the door. And in "The Last Roundup", Twilight slams the door in the face of a mailpony after getting a letter from Applejack. On his birthday. Granted, she was worried about her friend, but you can't help but feel sorry for him. (Pinkie Pie does give him a slice of cake, though.)
When researching the Mare in the Moon, she dumps a pile of books on Spike's head looking for the right one, and doesn't even notice.
In "Spike At Your Service" she once again is so buried in her work fails to notice Spike as he tearfully explains he is honor bound to serve Applejack and must leave her. She is visibly guilt ridden when Applejack later coaxes her out of her studies and explains what happened.
The episode "Dragon Quest" has Rarity telling Spike that he's better than the other dragons, because he has something special that they don't. Spike gleefully asks what it is, and then Rarity says he has "The cutest widdle chubby cheeks," unintentionally humiliating him in the process:
Rarity: Oh, isn't he adorable when he waddles off in anger? Spike: Waddle!? GAAHHH!
Spike himself has bouts of this due to his sometimes obnoxious sense of humor and inadvertent bluntness. He constantly aggravates Fluttershy's low confidence concerning her poor flying skills, but just doesn't get why Twilight keeps giving him nasty glares.
Fluttershy also falls into this category several times, such as when she makes Rainbow Dash's stage fright even worse in "Sonic Rainboom", describing how everyone in Cloudsdale, including the Wonderbolts and Princess Celestia would be watching her and see any mistakes she made.
The Cutie Mark Crusaders, when inviting Babs Seed into their club, make her painfully aware of her lack of a cutie mark, something she came there to forget about in the first place.
Futurama: Done repeatedly in "War is the H-Word", where Leela is pretending to be a macho guy, and Bender unknowingly "compliments" her on the macho stereotypes least suited to a woman:
Bender: You're my kind of soldier, Lemon. A foul-mouthed, barrel-chested, beer-bellied pile of ugly muscle.... But sweet girls aren't for you, eh? You hard-fighting, hard-farting, ugly, ugly son of a— Leela: Stop! Stop flattering me!
Cyborg in Teen Titans in the episode "Troq", when he calls Starfire by the titular word. Throughout the episode, the racist Val-Yor has been calling her this, and Starfire told Cyborg it meant "nothing" (without explaining that it meant "nothing" as in "worthless"), meaning he didn't realise how hurtful it was.
Becomes a case of Bullying a Dragon when you remember this is a race of super-strong beings who have Eye Beams and energy-hurling abilities
Korra from The Legend of Korra was trained for most of her life in a compound where she could be taught the four elements in safety, but as a result when she enters the world as a young adult she has No Social Skills and winds up greatly exacerbating a Love Triangle she winds up in because she has no firsthand experience with romance. At one point she plants a Forceful Kiss on her crush after he admits to liking her and honestly doesn't seem to grasp that it's a problem (at first), since he's already in a relationship with someone else.
In Sponge Bob Square Pants, we have the titular character himself. All though SpongeBob means well, he unintentionally ruins other peoples' lives. Just ask Squidward or his boating school teacher Mrs. Puff.
Moral Orel: Orel Puppington falls under this at times. He's actually a kid with good intentions, but as he's young, naive and often misinterprets advice from other adults, he usually ends up causing more bad than good for people.
Dee Dee of Dexter's Laboratory is this at her worst. For the most part, she's just trying to have fun, but she constantly ends up wrecking Dexter's lab and causing him no small amount of grief in doing so.
King of the Hill: Dale doesn't realize his son Joseph's true parentage, leading to this exchange with John Redcorn (Joseph's biological father):
John Redcorn: Joseph hates me...
Dale: Why would Joseph hate you? He barely knows you.
People with poor social skills — children and shy people who haven't had much chance to interact socially especially — are also prone to this.
Can also happen when you go to another culture. Even if you speak the language, the complexities of social interaction can take a while to learn, and it'll often involve a lot of unintentional insults to the people whose country you're in before you figure out what you should and should not do.
This can also happen in avowedly progressive circles. Black feminists frequently complain about the feminist movement focusing exclusively on issues that affect white, middle-class women and ignoring their own privilege. A book by well-known feminist blogger Amanda Marcotte contained racist illustrations from an old comic. Although Marcotte apologized and the book was reissued, the black feminist blogosphere has never forgiven her.