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This is a character who simply doesn't like to be touched, whether it be by a stranger or someone they know. They may be this way as a result of a bad experience, simple shyness, or because they just don't have the tolerance/patience for such things. Sometimes there's something wrong with them in a dangerous way and they know it. There's a good chance that they may be something of a loner as well. Sometimes they change for the better later on, sometimes they don't and sometimes the fact that they don't like to be touched isn't treated as a problem in the first place.
If it is treated like a problem, expect their Love Interest to attempt to fix it at some point. Most of the time, they succeed but the amount of blunders and time it takes depends greatly on the genre and nature of the story. At other times, they may already have a special person whose touch doesn't trigger any averse reaction, indicating a particularly trusting relationship.
In real life, this is called tactile defensiveness, and is common in abuse victims and people with conditions like ADHD or autism spectrum disorders, and especially with OCD, but even then, some people just don't like it and can't explain why. The perception that someone hates being touched can also come as a result of a Culture Clash: if someone believes that touching is an intimate gesture to be shared among close friends and lovers, then the American custom of shaking hands with someone the first time you meet them would be overly-intimate, akin to walking up to a complete stranger, grabbing their face, and Frenching them. Depending on culture and personality, attempting to touch the person could result in a Hand Off, the person stepping back to regain some sense of personal space, or an attack on the Personal Space Invader; however, adequately befriending them will usually remove the touch taboo in this case.
If someone like this actually lets someone else touch them, you can rest assured that something serious has just happened.
For instant hilarity, pair them up with someone that has No Sense of Personal Space or a Cuddle Bug. However, if you don't want them to punch you in the face, Air Hugging may be a better choice. May sometimes be a trait that Tsundere share.
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Anime & Manga
Lucy in Elfen Lied became like this as a result of her terrible childhood, though she doesn't mind if Kouta touches her.
Mayu also follows this to a degree; the manga implies that her traumatic experience with her stepfather has soured her on men in general, and finding Kouta in the bath groping Nyu doesn't help. Ironically, she appears to bond most closely with Bandou, who generally treats her like crap, except for when he saved her from the "Unknown Man".
"Father" in Fullmetal Alchemist has a mentality of not letting inferior humans laying a hand on him. Eventually, however, he did get physically ass-kicked by Edward in the finale due to his powers weakening.
Naruto: Sasuke and Gaara are the most prominent with Sasuke often proclaiming "Don't get so close!"/"Don't touch me so familiarly!" and Gaara threatening to kill people and/or giving the death glare. Gaara eventually got better about this, and Sasuke seemed to have stopped caring (maybe he just got used to Orochimaru grabbing him with snakes, and everything else seems minor by comparison).
Full Metal Panic!: Sōsuke Sagara, due to his highly paranoid nature. Most people know better than to try to get too touchy-feely with him. This is particularly obvious in that one episode of The Second Raid, where Kaname drags him out to get a haircut and he ends up holding the barber at gunpoint when his reflexes act up. In the same episode, though, it is shown that he is utterly calm about being touched by Kaname herself (who ends up being his personal hair stylist this way). Ironic, seeing how Kaname has probably single-handedly dished out more corporal punishment to him than all of his enemies combined.
Guts from Berserk, as mentioned in the quote above, as a result of being raped by one of his adoptive father's men during his childhood. The only exceptions are his Love Interest Casca and his more-or-less brother Griffith, and even Casca almost got strangled to death during their first time together due to Guts flashing back to what Donovan did to him.
During his stay with the Band of the Hawk, Guts did appear to be getting over this, as he became more chummy with his comrades and became more trusting of others close to him. Then the Eclipse happened. You can guess what state Guts reverted back into.
Based on this information, you can say that Guts' issue with people touching him has a lot to do with his trust in others, not just a single traumatic physical experience. After his time with Casca, Guts really doesn't talk about his childhood after that, but after the Eclipse, he goes back to hating being touched. It goes to show how much he felt betrayed by a man that he trusted, the second time in his life.
Once used for hilarity rather than drama, though. When he refuses to join the Hawks in a huge celebration after his first major battle with them, Pippin just grabs him, hauls Guts over his shoulder and drags him to the group kicking and screaming.
And as for Casca, after being raped into insanity by Femto during the Eclipse, she has shown signs of this herself. When Guts tries to touch her following the ordeal, she responds quite badly, both when she and Guts are with Godo, Rickert and Erica immediately following the Eclipse, and later in the Millennium Falcon arc after Guts' personal Beast almost gets him to rape her, where she bites Guts' hand and then hides behind Farnese, the only one who she seems to allow to touch her. Which only adds to Guts' misery considering how close they were before everything went to hell.
Ranma of Ranma ―. He gets extremely nervous when girls try to do something physical to him, and is vehemently heterosexual, which means he gets extremely violent if men try something on his "girl form". Part of the blame for this might be because he is inevitably battered by Akane if she sees him in something that looks compromising, while the other girls vary between aggressively flirting with him and hitting him for pretty much the same reason.
Of course he isn't above using the glomp himself as a tool to get an advantage on a rival or opponent, or standing on other people's skulls as a form of saying hello.
Yu Kanda from D.Gray-Man. Considering he spent his childhood up until about the age of 10 being used as a guinea pig for Body Horror-tastic experiments by the Black Order, this isn't entirely surprising.
Allen now qualifies as well, if only in one instance so far (chapter 215). He repeats, "Don't come near me!" after nearly killing Johnny as the Fourteenth. Quite a bit of self-loathing there.
This was also how Gokudera acted whenever Yamamoto, who has No Sense of Personal Space when it comes to anyone, got too close. At first.
Kaze to Ki no Uta: Rosemarine, by everyone except Jules and later Serge. Blame it on Auguste raping him when he was fifteen.
Setsuna of Gundam 00 is a Captain Ersatz of Sousuke of Full Metal Panic! (similar background as a Child Soldier) and shares Sousuke's aversion to being touched. Surprisingly, he extends this behavior to his Gundam as well, although he later grows out of it to the point he hugs Feldt and Marina without any sign of discomfort.
Hellsing: One of the things that sets off Seras Victoria is being attacked in this manner (in the anime at least).
Heine from Dogs: Bullets & Carnage has a bad reaction to being touched by women (except Nill for some reason that no one knows). Although his aversion for women is part of his traumatic backstory, it's played for laughs once when Naoto assumes that it's because he and Badou are in a homosexual relationship, and twice when Naoto faints and Heine should catch her but... doesn't.
Fate Testarossa of Lyrical Nanoha is often sensitive to being touched. In the manga for the movie, Linith notes that Fate is sensitive to physical contact, stiffening up when she hugs her, possibly due to a lack of parental affection from Precia. In Episode 8 of A's, Fate blushes and recoils slightly when Lindy lays her hand on Fate's to comfort her when she wakes up after having her Linker Core stolen.
Kouji Minamoto from Digimon Frontier. He even says out loud in episode two that he hates being touched by strangers.
Kazuma from Kagerou-Nostalgia either lashes out or shakes when touched by another guy after being attacked (and implied to be raped) by the demon Shimari.
Urabe of Mysterious Girlfriend X slips out of her boyfriend's hugs and tells him not to do that without asking first.
Right after using her (as Tsubaki called them) Panty-Scissors and uses awesome moves to cut whatever conveniently located poster next to or behind of him into tiny shreds.
Satellizer from Freezing, due to the abuse from her half-brother Louis. Touch her and she'll beat the ever loving shit out of you with her big blade. Unless you're Kazuya Aoi. This change when she got her Character Development but still show some sign of it.
Hyakujitsu No Bara: Taki in some scenes, where his reaction is either a slap or saying something along the lines of "Don't touch me with your filthy hands!" or "Know your place!".
Ciel from Black Butler. He appears to not enjoy physical contact, and has been shown slapping and insulting individuals for being too comfortable with touching or speaking to him. However, he tolerates Sebastian and does not complain when the demon picks him up or holds him. If he is stressed, he will also slap someone touching him away, proclaiming, "Don't touch me so easily!" This is a negative influence of the trauma he underwent during his time as a slave.
Ciel tolerates Elizabeth's physical contact, as well. The fact she's his fiancee, and has known him since they were little may have something to do with it.
Memori from Game X Rush. Possibly as a side-effect from his youth, where his family tended to treat him like a beloved pet (dressing him up, teasing him until he cried) than is probably good for a kid. Completely ignored in the second half of the manga, at least where Yuuki's involved.
Some might argue that this is far more due to his superiority complex than to abuse, especially since his reactions to being touched seem to imply disgust (if he reacts at all?) rather than anything resembling fear. I guess some could argue that he's hiding these reactions, but he doesn't hide all the emotional (some even BSOD) moments that he experiences when a feeling of powerlessness is forced upon him—all of which overtly have nothing to do with being touched or abused.
Ichise of Texhnolyze can get like this at times. If he's not comfortable with someone getting too touchy or close for his tastes he either gives them a Death Glare or has a tendency to go berserk. It seems that Ran's the only one who can touch him without provoking some violent response and even then he tends to tense up a bit. He gets better, somewhat.
Genjo Sanzo from Saiyuki is the grouchy antisocial type who is usually averse, rather violently so, to both physical contact and small talk even with his close friends, much less random strangers. This is because in the years he spent traveling, he was forced to kill to protect himself from bandits, and more relevantly, rapists. It's also notable that the only one he really lets touch him is Goku, and even then it'll put him in a pissy(er) mood.
Hinako from Bitter Virgin has this in regards to men due to suffering several years of sexual abuse by her stepfather.
Zettai Karen Children: Inverted trope. People go out of their way to avoid physical contact with psychometers. Sakaki expresses open jealousy that Shiho has people willing to hug her and hold her hand.
Galaxy Angel Rune's Apricot Sakuraba is like this around men in the sense that she can interact with men without difficulty, but if a man touches her, her super-strength kicks in and she literally reflexively kicks the man's ass.
L is probably one too, as hinted by the fact that he doesn't like touching either objects or people, and will only use his fingertips to do it.
Though L does tend to plant himself awkwardly close to other people, especially Light, and has no problem leaning straight into him - much to Light's blatant annoyance. L might be something of a subversion; he doesn't like touching objects, but people are fine.
Kyuubei Yagyu of Gintama is bad with being touched by men, however slightly. More often than not, she'll hurl any such unlucky guy.
Due to his shy nature, Rito from To Love-Ru doesn't like it when Lala or any of members of his Unwanted Harem cling to him.
Nabari No Ou: Yoite. Though he ends up allowing it of Miharu sometimes, "'Don't touch me" is easily the phrase he says the most.
Yukinari of Girls Bravo is heterosexual so he hates it if another guy touches him and he hates it if girls touch him because he has a bad allergic reaction that flares up whenever he is touched or beat up by girls. Miharu being the exception as she seems to be the only girl in the world that doesn't set off his allergy.
Kirie at times, especially if the touching is meant to be perverted.
Kira of Mars was raped by her stepfather when she was fourteen years old. As a result, she became averse to male touch and shy to the point of muteness.
In Tsukigasa, Azuma can't stand contact from other people ever since he was raped by his uncle. Since he never told anyone why, his Love Interest Kuroe was always trying to force him to get used to it.
Daryl Yan of Guilty Crown. He mentions a fear of infection at one point, but since he's just as leery about physical contact with clearly uninfected people, that seems to merely be one of many excuses.
Karakuridouji Ultimo: Jealous/Jealousy. Considering he nearly sliced off Yamato's arm after he touched his shoulder...
Due to her Tsundere persona Louise of Zero no Tsukaima often reacts violently and/or coldly when she's touched (especially if its in a perverted manner) or has her personal space invaded. Saito, being heterosexual, could get like this around guys but he doesn't mind if a pretty girl touches him (though he does mind if Louise is around when a girl touches him because that usually means he'll get punished by her).
Madarame from Genshiken is a bit uncomfortable around acts of physical affection.
Tsukasa from the oneshot Kuroneko Guardian due to being raped by a burglar.
Kyo of Fruits Basket is like this because he changes into a cat due to the Sohma curse whenever he gets hugged. He more or less mellows out about this in regards to Tohru who he falls in love with and eventually marries.
Inner Moka of Rosario + Vampire doesn't like to be touched. As Tsukune found out the hard way very early on in the second serialization.
Revy of Black Lagoon has a Hair-Trigger Temper and as such can be quite violent about being touched at times. It doesn't help that she was raped as a teenager by a police officer.
Jeremy in A Cruel God Reigns which is understandable, considering he is repeatedly raped throughout the series. Also falls along the lines of "Don't Look at Me!" later on both when he is working as a prostitute (he refuses to let customers see his back) and with Ian, although the latter eventually gets him to get over it because of the scars on his back.
Downplayed in Kannazuki no Miko: Himeko cannot stand anyone touching her hair—unless it's Chikane.
Shirotani from Ten Count has extreme mysophobia, so touching is basically an impossibility for him.
The original version of the Human Target had no fear, which can be a problem for someone who is setting himself up to be murdered.
The Boys: Only the Frenchman can touch the Female, and even he is only just barely allowed to. Anyone else... well, if she doesn't hate them, they might get away with nothing worse than several badly broken fingers.
X-23 is this, to the extent of lashing out with her claws when a friend touches her shoulder, and generally shows an aversion to physical contact, especially from those she's not close to (which is a very short list), justified by the abuse she suffered under the facility (see Real Life below). Laura has also described herself as "not a hugger" in All-New X-Men, which shows just how badly she's handling things when Laura is shown throwing herself into O5 Cyclops's arms to stop from entering a Heroic BSOD after being confronted with Arcade's footage of herself in a Trigger Scent-induced rage while in Murderworld. This becomes a bit of Character Development when she initiates one to try and comfort Teen!Scott, who is overwhelmed by Jean's kidnapping by the Shi'Ar, and the revelation his father is alive (Scott was brought to the future from a time before he learned his father was Space Pirate Corsair). Amusingly, Laura rejects a relieved hug from Teen!Warren later in the series for the same reason. Despite the fact they may have slept together.
Light: She placed her hand on my shoulder in a flirtatious style before she left. If I had the Death Note on me, I would have opened it up and would have written her name on it for touching me so freely. The first thing I would need to do when I got home is burn my clothing.
Hinata in A Demon In The Hyuuga Clan due to having no regular human contact with anyone (people go out of their way to avoid her since she's the Kyuubi's Jinchuuriki). Much to her dismay, Naruto enters her personal bubble with little to no warning. Since the story is from her perspective, the reader gets running commentary in these situations and she's shown as very unnerved yet confused by Naruto's exuberance.
Hinata: (thinking) "I turn around to see him running toward me, and he grins as he wraps his right arm around my neck, leaning on me like a good friend. I feel my cheeks flush at the sudden expression of friendship, and the close... personal contact the boy so willingly entered into with me."
Naruto: "Is something wrong Hinata-chan? You look flustered..."
Hinata: (thinking) He doesn't seem to his notice his right arm resting on my right shoulder, wrapped around behind my neck...
In Diaries of a Madman, Navarone generally dislikes being touched, though he does make more of an exception for more intimate touching. He tolerates it from some ponies more than others as well, and he does get better about this over the course of the story.
Bob in Retro Chill has a tendency to get startled whenever one of the aliens touches him... despite the fact that he's working with them.
Xenith, in Fallout: Equestria. Of course, given her history of brutal mistreatment as a slave, it's understandable. When she befriends Lil' Pip, she begins to warm up to the others, but never quite grows out of her phobia; even using a smoke grenade to escape a loving hug.
In Gensokyo 20XXIV, Ran after she was raped (which is Truth in Television), and it was to such an extreme that she almost put a small child through a wall. To a lesser degree was Yukari, after her experiences during imprisonment, that, at first, she didn't liked to be touched, preferring to limit if she wasn't going to not be touched but her behavior was comparatively different than Ran's, in that she behaved more like an autistic child would stiffen or push the person away, rarely if ever accepting it without feeling obligated or trying to imagine something else. However, she also had weakened vision at time, thus it would make more sense as she would startle easily.
Coraline Jones in Coraline, mostly because it is the Other Mother who initiates unwanted hugs and placing her hand on Coraline's shoulder, much to Coraline's discomfort.
Elsa in Frozen doesn't like being touched and doesn't touch other people because she is afraid of accidentally hurting someone with her powers. By the end of the movie, she has no problem touching people.
Film - Live Action
Suzie from Wild Things although it's possible she's just faking the trait, like she is with a lot of others.
Melvin Udal from ''As Good As It Gets to start with, with the exception of his love interest. He softens as the movie progresses.
Psycho from the movie Stripes announces that he'll kill anyone who touches him.
Lars from Lars and the Real Girl. Due to childhood trauma, he feels physical pain whenever he is touched by anyone... except, of course, Bianca.
Ardath Bey (alias Imhotep, the Mummy), from the original 1932 The Mummy:
Ardath Bey: Your pardon; I dislike to be touched — an Eastern prejudice.
The remake from 1999 has a Shout-Out to this. Imhotep is meeting with the Egyptologist who tries to shake his hand. Beni, acting as Imhotep's interpreter, stops him, saying, "Prince Imhotep does not like to be touched. Silly Eastern superstition, I'm afraid."
In Three O'Clock High, this is the reason why Buddy challenges Jerry to a fight after school. Buddy clobbers several other people who touch him.
The former half of David and Lisa is in an asylum because, among other things, he's afraid that touching people will kill him.
In Clara's Heart, the eponymous character freaks out whenever the main character touches her. This is because years ago, her son raped her.
It wasn't just any touching, though. Int his particular instance, she said her feet hurt so he started rubbing them. It was fine until he got up to her knees; THAT'S when she freaked out.
Used hilariously in Buffalo 66. The main characters are posing as a fake married couple for a picture (long story). The main character reveals he hates being touched and angrily tells his fake-wife, "We are a couple who don't touch!". The fake-wife in question? Christina Ricci.
The Demon from Paranormal Activity 3. When Katie accidentally bumps into it, it...doesn't take it very well.
Implied with Hanna, she damn well floors a guy when he tries to kiss her.
Nanon in The Unknown has a phobia about being hugged. This helps fuel Alonzo the Armless's insane belief that he is the perfect man for her.
Both India and Charlie in Stoker, as part of the bundle of vaguely antisocial traits they both share and that distinguish them as something of kindred spirits. India's discomfort may have something to do with her unusually acute senses, her uncomfortable home situation or the sexual harassment she suffers at school; Charlie's might well have something to do with growing up in a mental institution.
Leo Bloom from The Producers (1969 version) when he's having a panic attack, screaming "Don't touch me! Don't touch me!" when Max Bialistoc tries to calm him down.
Sparrow from Emma Bull's Bone Dance. It's because Sparrow is neither male nor female, and the only such person zie knows, so zie is sort of self-conscious. Unfortunately, one of Sparrow's best friends has No Sense of Personal Space, and Sparrow maintains this trait throughout the story.
Chronicles of Thomas Covenant. "Don't touch me!" is virtually Thomas' catchphrase, and his aversion to being touched is a good yardstick of how alienated or hopeless he feels at the time.
Jos from the Warchild Series hates being touched, and will flinch or jerk away if someone tries to, due to the abuse he suffered at Falcone's hands. He also has a tendency to back up if someone moves closer to him.
Relg from The Belgariad, a religious fanatic obsessed with his personal purity, is like this due to his fear of being defiled. His aversion to physical contact, and his companions' complete disregard for it, are something of a Running Gag. He gets better about it in the sequel, though - as his numerous children attest.
Charles in the Alpha and Omega series is his father's hitman. Given that werewolves occasionally go crazy and need to be mercy killed, he shuts himself off from social contact, especially physical contact, to prevent heartache if he ever has to kill them. The other werewolves all notice and give him his personal space. This causes complications in his relationship with his mate, who misinterprets his stolid demeanor.
Anna: "Someone told me you don't like to be touched."
Charles: "Not usually. But I love your touch. Touch me any time. Any place. Anywhere."
Raistlin Majere from Dragonlance tends to dislike physical contact.
Once to the point of snarling "Don't touch me! Don't ever touch me!" when his friend tugged on his sleeve. The poor guy just wanted to give him a present, too.
In Midnighters, Melissa hates being touched at the beginning of the books, anyway because she's a mindcaster. Physical contact "turns up" the person's thoughts.
In Dragaera Vlad Taltos's jhereg familiar "Loiosh", doesn't like physical contact with strangers. In Iorich, he thinks it's punishment to be petted by a young boy, and he expresses his distaste for being touched by a sorceress with a mental "Ewwwwwww!".
Kahlan Amnell, and by extension all Confessors, in the Sword of Truth series are an inverse of this: Nobody wants to touch them, because their powers work through physical contact. Because of this, Kahlan is initially very surprised that Richard offers to help her up when they first meet, since ordinarily nobody would want to touch a Confessor willingly.
The Demon's Lexicon: Nick. Attempts at familiarity (unless you're Alan) will probably end with a knife in the offending body part.
The Bug, who is autistic, in Matthew Reilly's Hovercar Racer will only tolerate being touched by his mother and his brother. A crowing moment of heartwarming is when he throws his arms around his very surprised father.
The Kni'lina in Mikhail Akhmanov's Arrivals from the Dark books value their personal space called "kono" to the point of obsessiveness. Kono consists of an area of roughly 5 paces. Only family members, sexual partners, doctors, and servants are allowed to violate one's kono. Any other violation of the personal space is a big cultural taboo. The Kni'lina can be easily spotted by their behavior, as they constantly look around them to make sure there's no one in the immediate vicinity. The prevailing theory for this behavior is likely a plague that wiped out much of their civilization centuries prior and the need to maintain quarantine.
From Jack Reacher we have Francis Neagle, the eponymous character's sergeant when he was in the army, actively avoids touching other people and having them touch her.
All of the psychics in 'Motherland' are terrified of physical contact. Probably because it inundates them with other people's unwanted memories and drives them insane.
Reek actually Theon Greyjoy in A Song of Ice and Fire hates being touched as a result of his torture at the hands of Ramsay Bolton.
In the V. C. Andrews novel My Sweet Audrina, Vera says this verbatim when double amputee Billie tries to comfort her as she cries. Whether this is a genuine feeling or if she's merely freaking out at being touched by a disabled person is unclear.
August from Of Fear and Faith mentions he doesn't like being touched and will always squirm or dodge out of the way before anyone makes contact. This does not apply around his stepsister Scarlet however, whose touch he enjoys and goes into some detail about in his narration.
James May of Top Gear (who might also have OCD) apparently dislikes physical contact, especially "man-contact"
Ned from Pushing Daisies doesn't like to be touched, even though he can touch living people with no problem. Not that surprising given he re-killed his mother by touching her, has spent his entire life having to avoid touching his dog, and that touching the wrong (dead) thing can have very unpleasant results. Also, Aunt Vivian for reasons unexplained.
Ben from Carnivāle, mostly due to being raised by a cold and uber-religious mother who told him he was "marked by the beast" because of his touch-based healing powers.
According to Lennier, the entire Minbari race from Babylon 5. Although some seem to be a bit more relaxed than him.
Tobias Beecher became like this because of all the abuse and horrible stuff that happens to him while he's in Oz. It's apparent in one scene where Keller comes up behind him, and he flinches when Keller touches him, much like an abused and frightened puppy would.
Chris Keller wasn't abused or hurt to the extent that Beecher was, but he does tend to shrug people off or shove them away whenever they try to touch him.
Also in Star Trek, Vulcans in general dislike direct physical contact with non-relatives. Justified due to their psychic proclivities and respect for privacy.
It's implied that Vulcans have some measure of tactile telepathy. Skin to skin contact without consent is implied to be viewed as an extreme invasion of privacy because it's tantamount to forcing your way into the other person's mind.
On the planet Capella women regard any physical contact as a mortal insult (presumably exceptions are made for husbands) punishable by death. The wife of the late Teer (chief) is furious when Kirk pulls her out of the way of a sword thrust. "He laid hands on me! It is my right to see him die."
When McCoy touched her stomach while trying to examine her (as she was super preggers, just about to go into labor), she slaps him. Twice. But he gets around this by slapping her right back.
Sheldon in The Big Bang Theory (partially because he's a germophobe). When he hugged Penny, it was the highest possible expression of gratitude for him. Even then, it was the most awkwardly made and hysterically tentative hug ever.
In the episode "Haunted", the UnSub doesn't like being touched because it brought back to him traumatic childhood memories.
"The Big Wheel" has an UnSub hates it because he was extremely obsessive-compulsive and germphobic.
Interestingly, in both episodes listed above, the killer touches or is touched by someone they're emotionally close to near the end of the episode, and for once, doesn't mind.
A few very observant fans have pointed out that Hotch almost never touches anyone (Jack, Hayley, and occasionally Rossi, and sometimes Reid) and when he does, it's usually a very emotional scene. He also tends to move away quickly when someone else touches him unexpectedly (the scene at the end of "Revelations" where Reid gives him a hug and his subsequent surprised reaction to it is the best example of this). It's implied that he was abused as a child in "Natural Born Killer":
Hotch: You were just responding to what you learned Vincent. When you grow up in an environment like that, an extremely abusive and violent household...it's not surprising that some people grow up to become killers.
Vincent Perotta: Some people?
Hotch: What's that?
Vincent Perotta: You said some people grow up to become killers.
Hotch: ...And some people grow up to catch them.
Reid himself too, as he can usual be seen side-stepping any offered handshakes with an awkward wave and only seems to let people he trusts (i.e. his team) touch him in any way.
In Persons Unknown, Joe (post-reprogramming) is this, to the point where he attempts to kill anyone who touches him. In one case ( The Night Manager's), he succeeds.
On the Law & Order: Special Victims Unit episode "Baggage", they learned from his file that a suspect hates being touched. So Elliot and Fin hold him down and threaten to rape him after he tries to get a lawyer. All this accomplishes is making the suspect wet himself and commit suicide with a small knife they did not take away from him. In case you were wondering the guy was a petty thief but completely innocent of the rapes and murders SVU was accusing him of.
Buffy the Vampire Slayer: Little known fact about Faith...she finds physical contact uncomfortable, due to her abusive parents. When she switched bodies with Buffy she was not used to Joyce hugging her, at all. She doesn't like Riley near her unless it's for casual sex. And she stabs Giles with a fork, before apologetically saying she doesn't like being pawed, unless she paws first.
Parker has no problem with getting up in people's space to distract the guards when necessary, but she once broke a guy's fingers for putting a hand on her leg. Parker certainly had abusive foster parents.
Eliot's background is more mysterious, but with him being the fighter of the team, it makes sense that he wouldn't want to let his guard down too much. (And like Dean below, he has no problem with touching women.)
Although he doesn't mind when his personal space is being invaded by a hot woman. Well, as long as she's not an evil demon or monster who wants to kill him.
You can usually tell how his and Sam's relationship is by how close he lets Sam stand. No chick flick moments, though.
On Without a Trace, the search for a missing autistic boy is complicated by this trope, as he fled from people who might otherwise have helped him whenever they made the mistake of touching him.
Emma Pillsbury from Glee. It's the reason she's a virgin.
Also Kurt Hummel (though not the virgin part after episode 3x05), who frequently dresses so that he is covered up from the soles of his ankles to the wrists and top of the neck, and who visibly flinches and pulls away from almost any contact with any character who isn't his father, his boyfriend or Mercedes, and has to brace himself and prepare to be able to give his other female friends hugs.
Michael from The Wire, due to being molested by his stepfather.
Jake Bohm in Touch will thrash and scream when touched, often accompanied by curling into a ball and breathing heavily, much to the sadness of his father, though on rare occasions he will touch someone voluntarily.
Patrick Jane on The Mentalist, though in a more passive-aggressive way than most examples. People who touch him uninvited can expect repercussions ranging from being mildly inconvenienced at a security checkpoint to being framed for murder and used as bait for a serial killer.
Daryl Dixon of The Walking Dead - he flinches back defensively when the least threatening member of the group leans in to give him a motherly kiss on the forehead. Word of God states that he's "constantly expecting to be hit" because of his abusive childhood.
Gary from Alphas hates being touched, due to his autism. Rachel's ability lends her to having issues with extensive physical contact.
In Angel, Bethany's discomfort with being touched clues Wesley in to the source of her telekinetic powers: she was a victim of incest by her father.
Tix, Rae's friend from the hospital in My Mad Fat Diary, can't stand being touched for any reason, to the point that she attacks Danny Two Hats when he innocently touches her arm in the canteen.
Doctor Who - The Twelfth Doctor, unlike most of his predecessors (even Nine, often regarded as the angsty one, was ready to hug anyone who asked).
"No, no, not the hugging! I'm against the hugging, please..."
Interestingly, this seems to encourage Clara to hug him at least once an episode.
In the finale of his debut series, the Doctor explains it's not the touching he minds, but the fact he can't see the other person's face.
Jade from Victorious will quickly and loudly point this out if the person touching her is anyone other than Beck, her boyfriend. Surprisingly enough, she's allowed Tori to touch her without screaming at the top of her lungs and has even invited it on occasion.
Eastern dragons are said to fly into an Unstoppable Rage against anyone who touches the "reversed scale" on their throat, to the point where "(touching a) reversed scale" has become an idiom for "(incurring) the wrath of a powerful person".
Stone Cold Steve Austin. As part of his persona, he will attack people just for patting him on the back. He's also been known to stare daggers at anyone who touches him, no matter what their intentions are.
The Witch from Left 4 Dead, to the point of violently slaughtering those who "startle" her.
Variation of this, Tales of the Abyss with Guy, who doesn't like being touched by females only. Later discovered to be result of him being buried under all his female servants and sister's dead bodies who protected him during an attack on his home.
This is played for laughs. Even after it's revealed why.
Presumably because he's also, openly and paradoxically, a Handsome Lech par excellence.
Connor from Assassins Creed III doesn't like being touched, especially by people he doesn't know very well, at one point shoulder-tossing one of his friends who approaches him from behind. A point of character development occurs when he learns and accepts to shake hands.
Squall in Final Fantasy VIII, as a symptom of his desire to avoid making emotional connections with people, usually ignores attempts to shake his hand and goes to far as to clock Zell on the head with the butt of his gunblade when Zell won't stop hugging him in gratitude for his timely rescue. When Rinoa sits in his lap on the Ragnarok, he awkwardly admits that he's not used to affectionate physical contact.
Alice of Alice: Madness Returns. Early in the first real-world sequence, there's a small side area where you can go. If you do, one of the children will mention this about her. Given what the "good" doctor in whose care she's been placed has been doing, it's small wonder.
Satoko of Higurashi no Naku Koro ni has been abused by her Evil Uncle so long and has such severe emotional trauma regarding the disappearance of her older brother that sometimes even the mere action of patting her on the head can lead to her having convulsions or reacting violently. Hate Plague is an ugly thing. Poor kid.
Suzushiro from Princess Waltz, although it only really applies to men, but it's not quite Does Not Like Men because she just believes she should save everything of herself (including skin contact) for Chris.
Hisui of Tsukihime, in honor of her sister. This is one of the reasons it's hard to realize the Twin Switch.
Darren, one of the potential Love Interests in Nicole, just about has a heart attack when Nicole asks for a hug when she realizes that he's Voix, the Rollr user she's been messaging back and forth with. He improves as the story progresses, though.
Due to her extreme OCD, Hannelore from Questionable Content cannot stand being touched by anyone. In early strips, Faye was extremely uncomfortable with any physical affection when she didn't expect it, including hugging.
Hannelore's aversion to being touched seems to only apply to humans (or perhaps creatures in general), presumably because biology is gross. When Momo hugs her unexpectedly, she starts screaming, until Momo points out that she's a robot, at which point Hanners immediately calms down.
Jessica from Candi cannot stand to be hugged because, in her childhood, her clinically psychotic brother repeatedly tried to vanquish the demon he thought she housed by strangling her with, you guessed it, hugs. She got better after she was (allegedly) about to break her crush's arm for hugging her unannounced.
JoeyVonKrause from Mortifer freaks out if someone touches him. William Aussek's freaked out reaction to a female prisoner coming onto him was originally theorized by fans as due to him being gay, but was eventually shown to be this trope when he was revealed to actually be Joey in disguise.
Mituna Captor of Homestuck really, really doesn't like it when Cronus touches him, and tells him several times, with an unusual degree of coherence, to stop doing so. He doesn't seem to mind being touched by Latula, but since Latula is his girlfriend and Cronus is the single sleaziest, creepiest dirtbag in the comic...
Nessiah of Dept Heaven Apocrypha had panic attacks when touched by others towards the beginning of the story, a result of his sexual abuse at the hands of Hector. Slowly, he's gotten better at handling it as long as he can see it coming, and doesn't mind Milanor touching him at all. The exception to this rule would be Kylier. It doesn't seem like he's ever going to get over that Mind Rape...
Summer Glau River Applewhite of Honorable Hogwarts cringes every time someone touches her, and occasionally has full-on panic attacks if she doesn't see it coming. The only person who can touch her without this happening is Vix. Which gives a whole new meaning to If It's You, It's Okay.
Isabel Guerra of Survival of the Fittest v4 seems to have problems with this. Flashbacks show her recoiling from touch and she screams and falls into a bush after brushing hands with Dave Morrison. It even has been shown to extend to other people being intimate, such as her pretty much having a panic attack when trapped in the restroom with Rosa Fiametta and Felicia Carmichael making out during prom.
Version three's Endgame also shows Maxie Dasai to be like this, not reacting well at all to being hugged. Given what happened to the character, it's understandable.
Ti'Cira Hawk and Ryori Holloway of The Gungan Councilhated any physical contact due to their time as slaves. It's become less of a problem now, though.
When Mr. Burns runs for governor on The Simpsons, one of his PR men tells them (the Simpson family), "Mr. Burns wants you to appear veeeery affectionate towards him. But we must remind you, he hates being touched."
One episode has Lisa put a friendly hand on the homeless/orphan boy you see from time to time, only for him to angrily pull away and yell "Don't touch me! Nothing gives you that right!" Played for Laughs despite coming off as mildly unsettling. (Also, it's from the infamous "panda rape" episode.)
Another episode had Homer dealing with a new supervisor (played by Jane Lynch) who was riding him hard. Ned Flanders recognizes her and tells Homer that she becomes violently angry when hugged, so he has Mr. Burns hug her during a ceremony. She responds by folding Burns into a ball.
Numbuh 363 in particular was so agitated about people touching him that it became a plot point. Numbuh One put a hand on Numbuh 363's shoulder while trying to teach Numbuh 363 a lesson about teamwork, and Numbuh 363 screamed "Don't TOUCH ME!!!" so loudly that it tipped Father off to their location.
According to the adult Numbuh 5, his reaction to people touching him is what led her to decommission Numbuh 363 once she became Supreme Leader.
Sam Manson from Danny Phantom has this in Flirting With Disasters; when Valerie hugs her Sam mentions that human contact does not agree with her. Yet, in other episodes, she shows no issues with touching people or being touched.
It's probably more Valerie contact that doesn't agree with her.
The Joker shows signs of this in Batman: Mask of the Phantasm when aging crime lord and former associate Sal Valestra grabs his collar while demanding his help against a vigilante killer that he assumes is Batman. The background fades to red as the Joker's expression contorts with rage...
The Joker then seems to have just been kidding about being angry, and he cheerfully reassures Sal that he'll help keep him safe from Batman. And then he kills Sal offscreen and leaves his grinning corpse for the Phantasm to find, so maybe he wasn't kidding after all.
He's not actually angry for being touched, but at Valestra for having the gall to tell him his "hands are just as dirty as mine! Dirtier even!"
Lemongrab of the show Adventure Time is angered by almost everything- ESPECIALLY being touched. When he raises his voice at Princess Bubblegum, Finn gives him a light slap on the hand and scolds him: "Watch your manners with the princess!" Lemongrab's eyes widen, and he SCREAMS in sheer outrage while clutching at his hand. Then he glares at Finn for a little bit, gasps, and rubs his hand some more, acting like nothing happened. Later, when he sends the candy castle staff to the dungeon, he gives Peppermint Butler FIVE EXTRA YEARS because Peppermint Butler pulled on the leg of his pants.
The title character of Daria; the main reason she and her boyfriend Tom don't sleep together in "My Night at Daria" is because she finds the idea of that much physical contact overwhelming. More surprisingly, this also seems to apply to her boy-magnet sister Quinn; she once chickened out of a modeling class that required suggestive poses with shirtless boys, and claims that she only slow-dances after the fifth date. It's notable that we almost never actually see her kiss/hug/touch a boy she's dating.
Home Movies - Coach Mc Guirk tries a team-spirit exercise where they all put their hands together - Fenton anxiously blurts "I don't like to be touched!" Brendon adds "I think we all have space issues..."
Grouchy hates being hugged in The Smurfs cartoon episode "A Hug For Grouchy" and tries to avoid hugs from those who don't respect his feelings, particularly on his most hated day of all, Hug-A-Smurf Day.
Francis from The Secret Saturdays. To the point that he has a forcefield that delivers an electric shock to anyone that invades his personal space.
This is often felt by victims of sexual abuse, particularly if they were a child when it occurred. Through therapy, they can overcome this.
Similarly, those who were victims of nonsexual physical or emotional abuse can also go through this trope. A physical abuse victim may be so used to being physically hurt that they involuntarily flinch or move away if someone tries to touch them, even if the person in question is not their abuser. Meanwhile, an emotionally abused person may have such low self-esteem that when someone tries to be affectionate towards them, they may feel undeserving, uncomfortable, or not used to it. Unsurprisingly, this causes a lot of problems if the victim desires to become sexually active, but therapy can oftentimes help to alleviate these symptoms.
People who have Autism, Aspergers, ADHD, or similar syndromes can fit this trope or No Sense of Personal Space. At times, they may individually bounce back and forth themselves depending on their moods or who they are with.
People who are hypersensitive or have very delicate skin may find that even a light brush or tap or poke by someone to be irritating, uncomfortable, or painful, and will go out of their way to avoid unnecessary physical contact with others.
Psoriasis can, though it does not always, cause flares where even normally comfortable, pleasant touches feel like being attacked by cat with untrimmed claws. Even soft cotton knit clothing can feel like sandpaper. Simple acts such as shaving and washing a face are agony.
Atopic dermatitis sufferers can find touch very painful, their skin can fissure or split from a fairly light touch.
Contact dermatitis suffers can have nasty skin reactions to residue on another person's hands because they are allergic.
People with the potentially deadly peanut allergy can react to residue left on another person's hands after consuming something with peanut products in it.
Horror Film Producer Val Lewton was known for a fear of being touched and served as the inspiration for the character Irena in his film Cat People, who was afraid of sexual arousal.
OCD sufferers and mysophobes (people afraid of germs) can have this trope. Howie Mandel provides a good example of this.
Many spiders are this, especially the shy black widow, who only bites when someone touches it.