In the 13th Detective Conan movie - "The Raven Chaser" we see Ran successfully dodging a bullet fired by a Black Syndicate member standing just in front of her. Truly one of her Crowning Moments of Awesome. A short slow-motion then happens, while we see this trope in use.
Happens twice to Kirika in Noir, once in the form of a bullet that grazes her head, apparently leaving her uninjured and undoing part of her Laser-Guided Amnesia, and again with a sword-wielding nun in the final episode. Mirielle also had one of these when she was a child, at the hands of then-Creepy Child Silvana; that's the apparent reason for her "half-bang" hairstyle.
Natsuki of Mai-HiME is angered to find that sword-wielding Mikoto has sheared off part of her hair with her giant claymore during their fight in the first episode. In this case we don't see the actual cut that takes it off, just the aftermath when Natsuki discovers it.
In a later episode, she does this to Nagi when she attempts to shoot him, but the bullet misses leaves a nasty mark on his hair.
Shizuru Viola in Mai-Otome has a sniper's bullet shot through her hair that takes out a spy she's captured (see the main page's image), though the damage is not noticeable by the next time we see her.
Meg from Burst Angel finds herself with a hole through her hair after Jo shoots through it to hit an enemy behind her.
In the special The History of Trunks, Trunks manages to cut off a small bit of Android 18's hair using his sword. She gets angry "My hair! It doesn't grow back!" then proceeds, with the help of Android 17 to beat Trunks to a pulp.
During Vegeta's battle with Recoome he tries to kill Recoome by blasting his head off with a ki-blast, but he survives the attack and it only burns off most of his hair.
Akane getting caught in the middle of Ranma's fight with Ryoga in Ranma One Half, and the subsequent haircut, is an example that overlaps with Important Haircut.
In one episode of Pokémon, a Scyther lops off part of Jessie's distinctive hairdo, and she becomes obsessed with getting even with the Pokémon. Not only does she fail, but the Scyther ends up giving her, James, and Meowth mohawks in the end.
In another episode, a Seviper that Team Rocket is trying to catch does the same thing. Jessie beats it into submission with her bare hands, then captures it. She's had it for seven seasons (spanning two series) since.
Shaman King uses this on Bokuto no Ryu as a running gag, as his Elvis-esque pompadour is cut repeatedly. Very rarely is his pompadour ever intact, though he will go to absurd ends to cover up his mangled hair. (In the manga, he claims to use the hair-care product "Wrongain", obviously a Rogaine-spoof, to quickly grow his pompadour back.)
Speaking of Nanoha, you can barely see it (it's one of those "pause it and THEN you'll see it), but in Nanoha and Fate's climatic battle, some of Nanoha's hair is shot off by Fate's Projectile Spell.
Laputa: Castle in the Sky features Sheeta losing both of her pigtails after Muska shoots them off. Also a rare case where the hair being targeted is intentional — he's doing it as a threat and says her ears are next. This is also a case of Important Haircut.
During one of Teresa's fights in Claymore a few strands of her hair are seen blowing after her when Ilena attempts to attack her. However, this isn't so much hint that she's losing her composure (quite the opposite) but to show that she's just that good and they can't even touch her.
Another example occurs when Clare rescues Galatea from Agatha's clutches ? Clare's Windcutter nicks off a bit of Galatea's bangs, prompting Galatea to snark that her rescuer's technique needs refining.
A variation occurs in the second episode of Zombie Loan: The cleaver that cuts off one of Michiru's braids actually does hit and fatally wound her, subverting the "close call" aspect. But she's later resurrected and cuts the second one off herself.
In the first episode of My Bride Is a Mermaid Nagasumi loses a few strands of hair when a dagger hits the wall close to his head. In a later episode, Akeno actually slices the top of his head off.
In D.Gray-Man, Lenalee Lee's formerly long Girlish Pigtails are burned off in a close call during a life-threatening over ocean battle with a level 3 Akuma, leaving her hair extremely short and unkempt in the process.
Occurs in Elfen Lied to multiple characters (mainly Lucy and Nana). However more often than not, people do get dismembered and sliced in half a lot.
Mikuru is subject to one of these during the baseball game when she ducks a fast moving baseball headed straight for her head. Not too long after, Yuki experiences the same thing, excepts she does it while standing comfortably at attention and catches only the balls that head straight for her face and other vital spots on her body.
And Yuki gets another two from Mikuru while filming the movie. Not by baseballs, not by BB pellets, but by pressurized water balls, which promptly decimates the landscape behind her. AT POINT BLANK RANGE.
In the Kinos Journey novels, the young Shishou's hair has a ragged, gunshot appearance◊, as though this is the only way she cuts her hair. Given the way she's been known to cut down trees later in life, this is perhaps unsurprising.
Also, in the first coliseum fight, Kino faces an assassin with a bladed boomerang that manages to give her a tiny shave on the way back. Later Kino does this deliberately, clipping the hair of a Master Swordsman to test his resolve. He doesn't flinch.
In Hunter × Hunter, Biscuit gets one of her pigtails cut off in a fight shortly after she is introduced. She continues to sport one-and-a-half pigtails for a while afterwards, before switching to a single ponytail.
Cardcaptor Sakura: Yue, after a mid-air scuffle with Ruby Moon, gets a portion of his hair severed by Ruby's swift hands.
In Full Metal Panic: The Second Raid Kaname Chidori is targeted by assassin Xia Yu Lan. Fortunately her knees buckle at that precise moment and so the bullet just clips her hair.
Played perfectly straight in Devil May Cry: The Animated Series when Trish and Lady fight in the church. Trish fires on a temporarily helpless Lady, who feels no wound and pats herself down, to find strands of hair on her shoulder. "You BITCH you shot my hair!" and the fight turns to fisticuffs.
It happens in One Piece in the fight between Zoro and Hatchan. At one point during his fight with Hatchan, Zoro lops off one of the spikes of his hairdo. For a few seconds, the octopus man looks as if he's about to blow a gasket, but then he immediately calms down as he realizes "It's only hair, after all. It'll grow back."
Death the Kid in Soul Eater had once some of his hair cut off during a fight. However, since he's very obsessed with balance and symmetry, it was sufficient to knock him out.
Hisagi did it to Findor who was a little unsettled by it but didn't go berserk.
In the anime, Toushirou managed to slice off a chunk of Gin's hair during their fight. Gin just carried on smiling...
It appeared as though Tsukishima had sliced off some of Orihime's hair when he cut her until it turned out he'd done something else instead. She fixed up the hair damage with her powers. He did, however, slice off some of Riruka's hair when she blocked his attack of Ichigo during his Villainous Breakdown triggered by Ginjou's death. In addition, thiss time he also cut quite a bit of her shoulder off, and she had to be healed by Orihime.
In Fushigi Yuugi, a few strands of Tamahome's hair are severed (in addition to him getting a slash across the cheek) while saving Miaka from thugs, just to show how badass he is. Note that this happened before his fight with Suboshi, resulting in his Important Haircut.
This is how Goku lost his long hair in Saiyuki, when Gojyo first activated the shakujo staff without knowing how to use it.
Lelouch's hair gets clipped in Code Geass when a completely broken Shirley shoots at him after being mind raped by Mao.
A Naruto villain seemed particularly ticked off every time her hair was damaged. Turns out it's because she's actually a body snatching wig. I.E. the hair is her real body.
Ushio tries to take out an enemy by tossing the spear... but only shaves off a few hairs.
Happens in almost every fight scene in Change 123. Everyone loses a few strands here and there, and yet it never adds up to a visible difference.
In Majin Tantei Nougami Neuro, Yako gets her hair clipped when Neuro uses her to demonstrate a "Slingshot Guillotine" (more visible in the manga).
In Wild Rock, Emba just barely escapes from the alligator he's trying to save Yuuen from. His Braid Of Action gets snapped clean off in the alligator's jaws.
Softenni has Kotone, in a fit of jealousy, manage to undo Coach Mishimagi's ponytail and cut off a part of his hair. With a soft tennis ball.
In Gunsmith Cats, Rally gets a goodly portion of hair from the left side of her head cut off when Gray slashes at her with his prosthetic blade-arm.
Joe from ARAGO - as he receives a pair of glasses that allow him to see demons, and sees Seth for what he really is, Seth responds with a glare that nicks Joe's cheek and cuts a few strands of his sideburns loose.
In one episode of Lupin III (Red Jacket), Goemon has left Lupin's gang for another gang whom he thinks fits his lifestyle better, since he has betrayed them, Lupin feels that he should kill Goemon. So Lupin fires a shot at his head, but Goemon ducks and the bullet grazes his cheek and cuts off a few locks of his hair.
In Slayers, Lina gets a magic suppressing tiara latched onto her head to prevent her from using magic or suffer a nasty shock. After she and Gourry escaped from their cell, Gourry finds their weapons, and without hesitation, tosses Lina up and slices at her face with his sword as she fell. It took of a small strand of hair, but ultimately sliced off the tiara from her head. Due to the pain, she repays him by bashing him over the head WITH HER OWN SWEATDROP.
In Upotte, Sako shoots off Sig's hair bun. Sig soon returns the favor by shooting off Sako's side braid, and letting her know that if she has to take a second shot, it'll be Sako's ear that comes off next.
Future Diary has a cop, Kurusu (4th), firing a shot at a terrorist, Minene (9th), during the Sakurami Middle School bombing.
In Jormungand, a lasting example occurs for Wilee: A bullet grazed his head during the First Gulf War, leaving a wound where hair didn't grow back in a distinctive rectangular patch. So, he buzzed the other side of his head to match.
In Fate/Zero, Saber loses a few strands of hair when she limbos under Lancer's spear to dodge a swipe. It's a very minor example, though, since her hairstyle didn't change at all from that.
In "Toriko" both Starjun and Midora subjected to that, due to having an enormously long hair.