When she hits him, he goes flying. Not just across the room or even across the yard — across town. Or to another state, or even another country. Sometimes he reaches Low Earth Orbit — or at least vanishes in A Twinkle in the Sky.
This is usually an adaptation of a one-panel gag the animators end up having fun with, although the usual treatment is to make it so over the top that it's not mistaken for real violence.
Compare Armor-Piercing Slap, which this trope is often combined with, or Hyperspace Mallet for another option an angry anime girl might try. If they're using a weapon of some sort, they may be a Home Run Hitter instead. Not to be confused with Rocket Punch, although it's only a matter of time before the two are combined. May cause a Nose Bleed if hit in the face, or if the character is being punched for seeing his attacker naked. If the victim is, in fact, completely and utterly innocent of such things and nothing naughty happened then it's an Unprovoked Pervert Payback.
Punched Across the Room is a more low-key, 'serious' version of this trope, despite being no less physically implausible.
Not to be confused with the Mini-Game of the same name from Kirby Super Star, and its remakeKirby Super Star Ultra, or the city from Fallout 3.
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Anime and Manga
F-Zero GP Legend included a memetic punch scene in which there is an explosion comparable in size to one-eighth of the galaxy, which both kills the Big Bad and acts as a Heroic Sacrifice for the Captain (He had an Unexplained Recovery by the GBA game.note The explosion was caused by something else, but that makes it less awesome, so we'll just pretend.
Akane Tendo (and most of the other female martial artists) in the anime adaptation of Ranma ˝. Not so much in the manga, but then the anime tended to exaggerate everything.
Also, Megaton Kicks are just as common as Megaton Punches. Sometimes the target even has time to muse on the current state of affairs and smooth out their clothing while sailing peacefully through the air.
Rekuta in Duel Masters. In the American dub, at least, he would be sent flying into the sky when he was so much as clipped by someone's bike.
Though it would normally follow a cry of "TODOMEDA!" from Shobu.
Even though it is not necessarily a punch (at least most of the time), Team Rocket on the Pokémon series always ends up flying into orbit (Team Rocket's blasting off agaiaaaaaaan!...*ting!*), even if the attacks that sent them weren't necessarily that powerful.
Love Hina often used surprisingly-involved animation for these. Its frequent use by Naru Narusegawa means this trope is also sometimes known as the "Naru Punch". Again, didn't happen as often or as dramatically in the manga, but much more frequently than in Ranma ˝.
In the first episode, Naru somehow manages to deliver the Megaton Punch... from the ground-level hot spring, up to the balcony where Keitaro was standing, two floors up, without her feet leaving the ground. As he flies off, Keitaro begs to know how she reached that far.
Then there's the scene where a nerd-disguised Naru punches Keitaro through a corridor with him bouncing off the walls and one doorframe (while every bystander just watches and stares without getting bowled over by him) before coming to a smashing halt at a closed door, one of many scenes that earned Keitaro his reputation of being immortal.
It turns out that Negi's mother Princess Arika did this a lot to Nagi.
Anya also did these several times to Negi... until he decided not to let her and reality ensued, showing him to be far too strong for her to be able to hit him otherwise.
One episode of Tenchi in Tokyo featured Amagasaki continually trying to talk to Tenchi and Sakuya, only to be attacked by the spirit of a female wrestler. While the wrestler used a different move every time, the result was always the same shot of Amagasaki flying off into the distant city, even when he was inside.
In Magical Project S, Ramia frequently does this to her little brother Rumiya to send him to Earth.
Subverted in Full Metal Panic!. Chidori hits Sagara, then the camera suddenly changes to the sky with a big contrail. This gives the impression that Sagara himself just left the contrail while crossing the atmosphere.
In Sengoku Basara, especially in the Heroes expansion, Takeda Shingen pulls this off and sent Sanada Yukimura flying. "OYAKATA-SAMAAAAA!!!!!"
In the anime adaptation, he did it again to Fuuma Kotarou, but since the way to the sky was obstructed by a castle, he crashed there, leaving quite a hole. Also later, his Megaton Punch catches on fire and turns Hojo Ujimasa into a twinkle in the ash.
In the anime version of Naruto, Sakura does this to Naruto in Shippuuden when he's being particularly perverted.
In Hunter × Hunter: Greed Island, Bisquit punches Killua this way whenever he makes a reference to her actual age.
In Fushigi Yuugi, the Nyan Nyan girls (Taiitsukun's assistants) often ended up in the receiving end of these when they seriously screwed up.
In Tona Gura, both Kazuki Arisaka and Marie Kagura, albeit through use of her paint-ball gun, can knock Yuuji Kagura clean across a room. Very very rarely, he can even become A Twinkle in the Sky. Subverted at least once, when Marie was about to punish Genki Girl Nina Isokawa. Yuuji effortlessly disarms her, and only gives her weaponry back when he shames his younger sister into attacking only him. Fridge Logic or Rule of Funny? You decide.
Seto no Hanayome has San's "Mermaid Voice", which isn't a literal punch but functions the same way.
Happens in the 5th episode of Higurashi Rei, where Keiichi gets punched into intergalactic space by Rena. The following punches to the rest of the cast, while not as extreme, also fit this trope.
Ran from Super Gals does this a number of times to multiple characters when the fights are comical.
THE iDOLM@STER - The Futami twins apply one of these on the Producer, calling it by name.
In the famous comic-book series Astérix, the magic-potion-powered Gauls frequently send Roman Legionnaires flying so high that they don't come down for several more panels. In the same vein, most of the time their sandals, shields and sometimes also the complete armour stays on the ground with their owner forcibly removed, so that when the legionnaire finally comes down, he does so in underwear only. It's convenient for Obelix, who, as a result of a bet in one of the early books, collects their helmets◊ as proof of having beaten more legionnaires than Asterix did.
The video game Asterix and Obelix: XXL and its sequel incorporate this: whenever an enemy is defeated, they fly off the screen at high speed, stretching like elastic. However, only a helmet (which constitutes in-game currency) is left behind, as opposed to a full set of armour.
Given that many super-hero stories are set in northeastern American cities, it's surprisingly common for a character to get "punched into Canada".
Alice's Fist of Death from Dilbert. Not always flying off, but she hit For Massive Damage. She once hit a guy so hard she knocked him into next week.
The Reality Warper powers also include punching a guy so hard everybody that had the same degree as him felt it, single-handedly taking out a army of robots and destroying the protein coat of a airborn virus.
Garfield used to do this a lot early on to other characters who made him mad including Nermal on one occasion one punch sent him flying into the moon.
Live Action TV
Hana of Kamen Rider Den-O is capable of punching anyone through the roof of a time-travelling train. Normally, the frequent victim of this would be the Imagin Momotaros. It doesn't stop him from Tempting Fate and pressing her Berserk Button multiple times, however.
In The Muppet Show, Miss Piggy sends Kermit (and anyone else, for that matter) flying with a karate chop whenever she's mad at him.
Guybrush Threepwood suffered this quite badly at the end of The Secret of Monkey Island, getting repeatedly punched into the air during his confrontation with LeChuck.
Amy Rose has her Megaton Hammer, which is useful for knocking around Sonic.
In Super Robot Wars Original Generation 2, Excellen playfully invokes this trope if you have her perform a certain mecha's punching attack, pretending that the enemy is her boyfriend being stubborn. The Original Generations remake even has her screaming out: "Kyosuke no BAKA!" as she delivers the final blow.
Seolla follows this suit when she rides the hot blood inducing machine Gespenst Mk II S. Have her execute the Gespenst Kick, and she'll pretend the enemy is Arado and yells out "A-ra-do no.... BAAAAKKKAAA!!" and delivers a Megaton Kick to the enemy.
In Original Generation Gaiden, first we have Folka's Iadabaoth which one move start with Rapid-Fire Fisticuffs but end with Punched Across the Room which broke the mountain in background. Then Shura King Alkaid's Raha Exteem ditch the spam part and just punch once, send enemy through several mountains.
Fire Emblem has one in Path of Radiance: when Boyd teases Mist for weighing more than Leanne, she knocks him across a pool of water and into a tree. The animation for the "Smite" ability, which, normally, is available only to the largest character in the game (disregarding shifted dragons), is used for this scene. The only other character to knock someone out with a shove is the friggin' Black Knight!
In Final Fantasy VII, there's a comic scene during the first few hours of the game where Barrett does a Megaton Punch on one of his allies out of frustration. This sends his ally flying across the room and onto the screen.
Dark Souls has the adult Mushroom People. They look fairly goofy, move slow, and up to that point you've been fighting the young versions, which are absolutely pathetic. And then they do this to you.◊
While she does it with a throw rather then a punch, Marina Liteyears, a Robot Girl with a powerful throw (to the point grabbing and throwing is her entire attack style) of Mischief Makers does this to her creator Prof. Theo each time she finishes rescuing him due to him trying to grope her. Another villain then grabs him and she has to do it all over again.
Sylvester the Cat was involved in two such fracases with two dogs – a bulldog named Spike and a tiny terrier named Chester, with Spike always getting the worst end of things. In the earlier short, "Tree for Two," Spike is thrashed by a giant panther who had escaped a local zoo and mistakes him for the much smaller Sylvester; Chester, showing immense strength for his tiny size, easily whips the puddy tat with – among other moves – the trope namer. The later "Dr. Jerkyl's Hyde" saw Spike (here named Alfie and given a British accent) get punched and beaten by Sylvester, who has mutated thanks to a hyde-type potion; again, Chester is able to easily beat up Sylvester.
"Lighter Than Hare" – Averted; Yosemite Sam (a space alien) boasts that not only are his "indestructible tanks" and "unbeatable robots" unstoppable, they are more powerful and cunning and can more easily subdue Bugs Bunny. Nope!
Pick a Popeye cartoon, and half the time, after pummeling the bad guy into a bruised, battered shell of a man (or woman... or alien...), Popeye will deliver one last, huge punch, often with humorous results upon landing.
The sometimes-seen Twister Punch is Popeye's own twist (heh heh) on the Megaton Punch.
In an episode of The Angry Beavers, Dag picks on his brother everyday until finally, Norbert gets so furious he literally punches Dag into last week...repeatedly. Finally, Dag ends up making him promise not to do it again, then accidentally ruins the end of his movie by spoiling the ending. Norbert keeps his word and doesn't punch him into last week. Instead... well, this quote will explain it.
Dag: *looks at the calendar* Hey...he didn't bop me into last week! *looks outside the window* Eeeh. If I may borrow a phrase from my brother Norbert....HE BOPPED ME INTO THE DAWN OF TIME!!!