Innocently Insensitive

Exactly What It Says on the Tin. This character (usually male) picks on the short girl for being short. He'll ask a woman for her age. He'll bug the flamboyant guy about his sexuality. And the worse part is, he doesn't realize what he's doing is rather painful for the person on the receiving end of the criticism. In the worse cases, he might not stop at one insult and even continue until someone forces him to stop, or the other person runs away crying. (His reaction to this is probably: "Huh? What did I do?")

What separates him from the Jerkass is that this person is actually a good guy - he's just clueless to things that people might generally be sensitive to. To him, it was just a fun joke - no offense intended. When others bring up the fact that what he's saying is hurting other people's feelings, he tries to change.

The Idiot Hero is prone to this. They tend to receive replies like You Know I'm Black, Right? and I'm Standing Right Here. Innocent Bigot is a subtrope. When this is done intentionally, they're a Deadpan Snarker. Obviously guilty of frequently committing a Fee Fi Faux Pas.

A frustrating Truth in Television. Especially notable are people with Asperger's Syndrome.

Anime and Manga

 * Monkey D. Luffy from One Piece.
 * Takanashi from WORKING!!
 * Yachiyo is like this, usually to Satou.
 * Yamada has her moments too.
 * Inuyasha has his moments.
 * Sai from Naruto post- Heel Face Turn and Character Development. He is trying to become better friends with Naruto and Sakura, but genuinely thinks "ugly" is a good idea for a nickname, and that people always need to hear the truth.
 * 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 entire 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 literally 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 due to the fact that Haru is a possibly immortal alien who struggles with understanding things from the view point of us Puny Earthlings.

Literature

 * 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 just about 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.
 * Note that, 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.
 * Brainless Beauty Christine from the Discworld book Maskerade, an opera hopeful with the looks but not the musical talent, is apparently oblivious to the fact that her very presence is trampling over the ambitions of Fat Girl Agnes Nitt, who has the musical talent but not the looks. She also says at one point that Agnes is lucky about not having to watch what she eats.

Live-Action TV

 * Sheldon from The Big Bang Theory
 * Liz Lemon during High School, as revealed in the Class Reunion of 30 Rock. (More rarely, she does this in the present as well.)
 * 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 totally 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.
 * Much of the cast of Friends at one point or another, but especially Joey and Phoebe.
 * 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.

Video Games

 * 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.
 * Shizune Hakamichi from the Visual Novel 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"
 * 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 routes; in the former,, and in the latter,.
 * Sakuya Shirogane Le Bel. 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.

Web Comics

 * 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.

Western Animation
"Rarity: Oh, isn't he adorable when he waddles off in anger? Spike: Waddle!? GAAHHH!"
 * 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 frosty 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 caused the termination of Nightmare Night in "Luna Eclipsed" and she's only concerned about candy!
 * 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.)
 * 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.
 * Also:

"Girl: Hey Tyler, you going to algebra? Tyler: Yeah, I'll see you there. [The girl instantly breaks down bawling, then leaps out a two-story window] Girl's friend: You're awful! Narrator: The preceding joke is brought to you by: Men. Invisible Backup Band: Men! We don't know what we did!"
 * Parodied in a Family Guy skit about high school kids (and no, this isn't taken out of context):

Real Life

 * As noted, a Truth in Television for people with Aspergers Syndrome and Autism.