In Naruto, this is especially noticeable when characters are leaping through the treetops. As this is usually a prime opportunity for exposition, a character can remain airbound in a mostly horizontal leap for upwards of ten seconds before touching down on another branch.
Even Fullmetal Alchemist doesn't avert this trope. It's especially apparent with the Xingese characters.
In Samurai 7, the samurai express improbable leaping prowess necessary to enable them to take down Nobuserai the size of houses.
Rurouni Kenshin: Kenshin - and many other characters in the series - can jump so high in a single bound they leave the vision of mere mortals. At least once Kenshin saves a character from falling off a cliff by jumping down after them, overtaking them, grabbing them and leaping back up from the bottom of the cliff.
The Tokyo Mew Mew anime takes it to ridiculous extents. Besides incredible jumping abilities, sometimes the girls are actually given hovering powers so they can keep up with their flight-capable enemies. This makes one wonder where this leaves Mew Mint, the only member of the team that is supposed to be able to fly.
The girls from Gunslinger Girl can jump very high, as exemplified by both Henrietta and Triela. Henrietta actually performs this feat most impressively to chase someone on a scooter after he steals her purse.
Somewhat weird example... Pinoco from Black Jack has frequently demonstrated the ability to leap more than 3 times her own height - which is, of course, necessary for her to properly Glomp the titular character. It gets stranger when you remember that her body is mostly artificial, making her a good deal heavier than a normal person (to the point where she sinks like a rock in water), and while being partially cybernetic would generally be a justification, Black Jack generally treats replacement limbs with a decent degree of realism. Considering Pinoco's uber-squicky origin, however, nobody really wants to dig into her physical capabilities too much...
When she was (spoilered for squick) a teratoma, she was telepathic. Maybe it just changed forms.
Also seen here combined with a Flash Step and a Wall Jump to let Kaede travel 750 meters (750 m = 820 yd) in a single bound, in less than the time it takes Mana to work the bolt.
Fushigi Yuugi exhibits this trope, from Tamahome (who leaps up to the top of a very high palace wall and even leaps over cars in heavy traffic), to Tasuki (who chases the person they first believed to be Chiriko but is really the Seiryuu Seishi Amiboshi in disguise across the city from roof to roof with Tamahome), to Kutou spies.
The titular warriors from Claymore can jump really, really high. Clare, who's supposedly the weakest of all, can do some serious Roof Hopping, whereas Teresa, supposedly the strongest, can jump several kilometers in one leap.
Pokémon tends to leave implausible acrobatics to the non-human characters, but one episode in particular has Ash make what has to be a five-story jump into Team Rocket's balloon, which looked exactly as ridiculous as it sounds. The weird part is the character of the day had a Metagross that had to help him down with telekinesis. Why didn't they just have it toss him up there in the first place?
DearS, justified in that the DearS have gravity-manipulation abilities.
Neon Genesis Evangelion, where the Eva units make some mighty impressive leaps. Example: Eva Unit 2 jumping from ship to ship.
Just try the Evangelion mod for UT2004, I dare you. Specifically, the "Racing" power mode.
Ninku, Aicho is the sky captain but often has to use his amazing leap talents for ferrying people on his back when they need to cover major ground.
Like all good superheroes without flight but with super strength and speed, Kiddy Grade's Éclair can do this too.
From Beyblade we have Mystel who appears to flow in the air when he jumps. Also Kai is called out by Kenny in the manga because of his crazy jumping ability.
This sort of thing was commonplace in Dragon Ball before they introduced actual flying to the series. A particularly good example is during the 21st (21 stone = 294 lbs) Tenkaichi Budokai where Goku and Namu attack each other while falling from the sky after jumping so high.
In the first episode of Heroic Age, Belcross jumps from the ground into orbit to attack a Bronze tribe hive ship. In a nod to the physics that would actually be involved in something like this, Belcross kicks a crater probably a kilometer wide into the ground when he jumps.
A honorable mention must go to Action Girl Nami of One Piece, who does a series of long jumps over city building to reach to her captain, who is stuck between two buildings, while a storm is impending.
A more true example is Brook. Having died once and come back as a skeleton, Brook has all of the strength he did before, but without the mass of those pesky muscles, organs, and skin weighing him down; this results in him having amazing speed, the ability to run on water and, more importantly for this trope, the ability to jump distances that are impressive even by One Piece standards. One of his earlier scenes has him getting thrown from near the top of a fairly tall building, only to jump right back up to play Big Damn Heroes to Robin and Franky.
The Twilight of Gangsta love to show off how badass they are through this trope.
A Certain Magical Index: Accelerator can do this, either by amplifying his vertical motion vector... or by simply cancelling gravity's effect on himself. He can fly too, but jumping really high is a lot simpler (flight involves mini-tornadoes and lots of complex wind vector calculations).
The dogs from Ginga Nagareboshi Gin have jumped over plenty of gorges, usually succeeding with one leap. Just see how stunned they looked when they see a puppy fly over the gorge!
Superman, the Ur Example, had "leaping tall buildings in a single bound" among his three original powers. In the comics, Supes' original maximum leaping distance was an Eighth of a Mile (660 ft or 201 m (201 m = 220 yd)). It became straight-up Flight when the Fleischers found it more impressive animated. Especially since it was basically treated as flight anyway.
However, it's worth mentioning that the boy in blue still has this power separate from his flight ability.
In the Grant Morrison-writtenAction Comics relaunch, when Clark first started off as Superman, he had yet to learn how to fly, and is still simply leaping tall buildings in a single bound.
Doomsday can do this, in a manner similar to the Hulk.
Technically, any character with Super Strength should have this as a bonus, due to how hard they could push off the ground.
Averted with The Thing. His rock-like body gives him Super Strength, but also makes him too heavy to be able to use this trope.
Parodied by The Tick in both his name and lack of flight.
Empowered lampshades this by having Ninjette, not Emp, being good at this. Its justified in that 'Jette is, as her name suggests, a ninja. When Emp flails wildly during a training period with 'Jette, demolishing a number of trees and branches, she is not amused.
Emp: You ninjas always make this treehooping crap look so easy in the damn anime...!"
The Incredible Hulk is a rare North American example, stated to be able to leap 3 miles. But then, the guy can also throw tanks.
Hulk can also jump to the moon.
Given that Hulk's super leaping is a simple application of his strength, and his strength is inherently variable based on how angry he is at the moment, piss him off enough and he can jump as far as he feels like.
Which is quite clever if you think about it. The further Hulk gets from the thing that makes him angry, the calmer he'll be. So he'll be jumping less and less distance each time. Then the army or SHIELD or whoever is chasing him will catch up, piss him off again, and the whole cycle repeats.
Spider-Man leaps through the air like a spider can.
Wolverine also displays this power in the 2008 video game.
Check out the GLX (Great Lakes X-Men) Christmas Special to see what happens when you have this power and don't really pay attention to maximum height, especially when you don't have protection against re-entry.
The original version of Paperinik, Donald Duck's superhero alias in Italian Disney comics, uses special boots with springs in them to jump tall buildings etc. It is basically his "signature gadget".
The Red Bat too.
In Alan Moore's Supreme, one of the older versions of Supreme can't fly, but "has these incredible leaps", since they're all just expies of different versions of Superman.
Slingers member Prodigy had this as one of his powers, using his cape to help his glide...somehow. It was mentioned at least once that people weren't sure whether he was flying or leaping.
The Sailor Moon fanfic Tacky Yellow No-Name includes a showdown between Tuxedo Mask and Kunzite, the latter wanting to become a Mysterious Protector now too. They try to best each other at the ability to jump onto increasingly high and difficult locations while spouting odd and mysterious bits of wisdom. About the time that it devolves to "Never run with scissors!" Kunzite makes the unfortunate decision about where to jump:
Tuxedo Mask: Impaled your foot on the weathervane, eh? Amateur.
Paul in With Strings Attached can jump like a champ. At low power, putting some effort into it, he can jump at least 50 feet straight up. At high power, without putting much effort into it, he can jump at least a quarter of a mile.
Commenting on Paul, Jeft notes that he had to work out how to scale down Paul's strength lest he be completely incapable of moving without causing massive chaos. Hence, he cannot leap nearly as far as his level of strength would indicate. Otherwise, a simple step that might have taken him, say, two feet as a normal person would take him over 4,000 feet at full power.
Unlike most fictional big jumpers, Paul also (more or less) obeys the laws of physics, in that he makes a mess when he jumps as well as when he lands. In a Crowning Moment of Funny, he and John scream at each other about Paul's reluctance to power-jump off a ledge where a bridge had been, on the grounds that the inhabitants might want to rebuild the bridge someday and will need that ledge.
Film — Animated
The Land Before Time: Sharptooth jumps on top of a large cliff in attempt to kill the kids, who are trying to push a boulder on him. They still kill him anyways with the boulder.
Before that, he was able to leap on top of Littlefoot's mother and kill her.
Turkish Star Wars. By the third act, the protagonist seems to spend entire fight scenes jumping over his enemies.
Anyone in The Matrix can jump like this, while Neo later flies. However, when he first tried to jump between two skyscrapers as part of his training, he failed miserably... just like everyone else on their first time.
In Mistborn, one of the allomancy powers allows you to push off metal rods embedded in the ground.
Live Action TV
Angel does this occasionally in the later seasons.
The Beast did this to a much more dramatic degree, making his exit from scenes by launching himself high into the night sky Superman-fashion.
Buffy the Vampire Slayer did this on occasion. In an early episode she jumped over a gate twice her height without a running start, and jumped her way onto to the top of a clock tower (although this did take more than one jump).
Birds of Prey often has Huntress display this power, but there is a particularly egregious example in the final episode, where two other characters jump to the second story, one of whom is paraplegic.
Power Rangers have been leaping hundreds of feet into the air since the very beginning. (And, by extension, the Super Sentai series)
George (to Jim, after he tries to fly and falls off a building): "YOU CAN'T FLY! ... But you can jump!"
The Most Extreme had an episode called "Jumpers", which featured the top 10 jumpers of the animal kingdom.
In Smallville, Clark can't fly until the finale episode, but can jump high and far, starting with his first real super-leap in the episode "Insurgence", leaping from the Daily Planet building to LuthorCorp Tower. His super-leaps become more powerful as the series progresses. It's hinted at during the run of the series that he possesses the ability to fly before the last episode, but just can't for some reason. (In reality, it was the "No Tights, No Flights" rule.)
There's numerous incidences in the show of Clark being under various mental states (like red kryptonite) where he is able to fly, yet once he returns to normal he can't (and frequently can't even remember doing so). He can't seem to imagine himself having the ability of flight.
All vampires can do this in Moonlight, although their leaps are weak by comparison to someone like Superman. Mick's limit appears to be 5 stories. An old vampire is shown to be able to easily jump down from a high-rise without problems (also, without ruining his shoes). It's also implied that he got that to the balcony by jumping.
Blade has vampires jump fairly high. The pilot has Krista try to kill Marcus van Sciver with a silver bullet fired from a sniper rifle atop a tall building. Van Sciver's Number Two knocks Krista out by coming from above (there are no taller buildings in the vicinity). The Grand Finale also shows Van Sciver and Blade having a sword fight at a big meeting hall by jumping all over the place.
In Exalted, everyone can do this trope according to the tables. Then you can get an even more super version of the power for really high jumps.
Specifically, distances are measured in yards. You can jump your Strength + Athletics in yards vertically, and twice that horizontally. Even the least combat-oriented, freshly-Exalted (since up until the point of Exaltation you are a mere mortal) scholars and diplomats can jump abnormal distances. A yard is 3 feet and roughly 0.9 meters (0.9 m = 35.4 in), for those unfamiliar with it. The other more combat-oriented Exalts truly can leap considerable distances in a single bound.
The Athletics Charm Mountain-Crossing Leap allows one to jump (Essence x 5) miles in a matter of minutes. The minimum Essence for this skill is 4, so 20 mile jumps are the standard for this specific Charm.
"Boots of jumping" are magical artifacts which turn up in many computer and role-playing games, and let characters demonstrate this trope. The idea probably started with Dungeons & Dragons, although D&D called them "boots of striding and springing".
Dungeons & Dragons' Third Edition also gave the monk the ability Leap of the Clouds, making your jump distance dependent only on the Jump check, not any other factors. 3.5 removed it, but then also removed all restrictions on how far you could jump based on anything other than the jump check. Since Jump was dependent on your Strength, it was presumably reasoned that if you had superhuman strength you deserved to jump really high.
The Jump check is also dependent on how many skill points are invested in the skill, which is limited by character level. The skill also receives bonuses based on the character's running speed. If a player really wants to, it's not terribly difficult to get a thirty-foot vertical standing jump at mid-to-high levels.
The Pathfinder RPG (based on D&D3.5) has monks that gain a bonus equal to their level to their jump checks. Plus the bonus they get for having a high speed. Plus their ranks in the Acrobatics skill (based on DEX rather than STR). Plus the bonus for it being a class skill. Plus they don't take a penalty for not having a running start. Oh, and they can spend a Ki Point to get an instant +20 to the check. This boils down to a 5th level Monk being able to make a 10' vertical leap, from a standstill, when they roll a 1 on the die. That's not jumping up to grab the ledge 10' above you either, that's landing on it with your feet. Bigger leaps get easier as they get more skilled and faster, and gain magical equipment.
The above has a really fun glitch where making that Jump check can also serve as a wide-area Charm Person on crack. When CO says "Jump Good", they mean it!
GURPS has the Super Jump advantage, which doubles jump distance with each level.
For skill based jumps, you can choose the jumping skill, the half of which can replace the usual number used for jumping distance. And there is also flying leap, which triples both the distance of the jump and the damage you deal if you use it as part of an attack. This is balanced by only allowing it to those with the Trained By A Master or Weapon Master advantage.
Champions has always had a characters' base jumping distance based on strength. But to really invoke this trope, add extra leaping distance and a non-combat multiplier. And you can take an accuracy advantage, so the character never misses their chosen landing spot.
Feng Shui's Path of the Leaping Storm fu path is all about emulating the classic Wuxia swordsman, and the first two powers of the path are Prodigious Leap and Abundant Leap, both of which allow a character to do crazy flying wuxia leaps.
Mutants & Masterminds offers the Leaping power which multiplies your leaping distance by rank. You start at 2 times your normal jumping distance. Rank 10 is 2000 times your normal jumping distance... and there's no upper limit, although longer distances mean you may take a while to get to your destination. Flight is faster, but not always as cool as being able to jump to the moon.
A clarification from the game creator indicated that the bonus to jumping given by the Acrobatics skill applies before the multiplier, so with a few fancy flips, you may be able to travel a few miles further...
Essentially any side-scrolling video game, going back to Donkey Kong and probably earlier (excluding games where the player controls a flying vehicle).
Super Mario Bros.: Practically everybody. Mario and Luigi are the second-best and best jumpers, respectively.
Lara Croft in the early Tomb Raider games, though more recent installments have toned down her jumping ability to a more realistic level.
Actually averted in Mass Effect, the only time anyone ever makes any kind of implausible jump, even in cutscenes, is while escaping a spacecraft in a high parking orbit where the gravity is pretty darned weak.
Even characters without jump-related super powers can leap over chain-link fences as tall as themselves.
Most fighting games involve implausible jumping skills involving characters who can, from a standing position, reach vertical displacements of several times their height and great distances forward.
Bushido Blade notably averted this, allowing the players to barely manage to jump their height, and that only with the lighter characters wielding smaller weapons.
Probably the most extreme are some of Capcom's Versus games where you could literally jump to heights around 50 times the height of your standard character. Even more impressive for the miniscule Servbot, who is jumping at least 200 times his height.
Various Metroid games have the Space Jump Boots and/or the Screw Attack, which allow you to jump off of thin air once and/or many times. Combined with Samus' ability to jump several yards already, this makes for some impressive heights.
Many Final Fantasy games have a Jump command, traditionally having you jump high enough to avoid any friendly or hostile attacks or spells, then landing pointy-end-down on a foe; typically, the Jump attack does double damage, but only if you're using a spear. If the game in question has job classes, like Final Fantasy XI, the Dragoon/Lancer/Dragon Knight class will always have this ability. If the game doesn't have specified job classes, such as Final Fantasy X, then the ability will belong only to characters who wield a spear of some sort, which is the weapon of choice for, yep, Dragoons and their kin. It's never really explained as to how these characters can survive such leaps and falls, however. It isFinal Fantasy, though...
The most notable examples are in Advent Children. First, in the battle with Bahamut SIN, where the entire party (Except for Barret) leaps into the sky to be used as stepping stones for Cloud to go after Bahamaut SIN. Second, the climatic fight between Cloud and Sephiroth, with Cloud leaping all over the ruins of Midgar and the Shinra Building.
In the first instance, with exceptions for the genetic experiment (Vincent) and lifelong ninja (Yuffie), a popular fanon theory is that Barret is throwing them.
In Crisis Core, the cutscene involving the 'play' duel between Sephiroth, Genesis, and Angeal, in which all three make improbably high jumps.
This is displayed even out of battle in Final Fantasy IX wherein the game's two dragon knights, Freya Crescent and Fratley Irontail, easily leap from rooftop to rooftop and leap four to five times their body height from a complete standstill. Even the most athletic members of the party can't keep up. (Although this could be somewhat explained by the fact that the dragon knights are a non-human race of rat people with supposedly much greater leg strength than humans.)
8-Bit Theater has a Dragoon with the ability to make insanely high jumps... so long as there is someone to land on. It is a jump attack, after all. In keeping with the series, Black Mage is the usual landing spot.
It also seems that he needs his spear, as after it accidentally got teleported away (it was stuck through Black Mage at the time), he hasn't jumped even once. He also commented "I needed that spear".
Both played straight and subverted in Final Fantasy X-2, where the three protagonists have no qualms about jumping hundreds of feet into and out of huge gaping holes down to the core of the Fayth, yet in one cutscene, as Yuna prepares to jump off a cliff in the Mi'ihen Highroad to save some civilians, Payne stops her and forces you to take a long windy path down to the bottom of said cliff.
Spoofed in Morrowind: if you head north along the swamp road, you'll hear a noise behind you, and when you turn around, you come across the body of a magician. If you check his possessions, you'll find three scrolls of Icarian Flight, which temporarily boosts your acrobatics stat and lets you jump great distances for a while. Landing safely after the spell wears off is another matter...
However, it IS possible to save him if you go out of your way to avoid that area, create a Slowfall spell, and cast it on him once you see him flying to his doom. He'll only say "I don't want to talk about it." after he lands and the only way to retrieve the scrolls then is to either kill him or steal them.
Spoofed but not completely averted; it's still possible to reach absurd jump heights without the above spell. A master acrobat with a strong jumping enchantment can obviate Levitation spells and bound across the land, avoiding any random encounters (and it's a hell of a rush.) This was toned down in Oblivion to prevent players from vaulting the city walls that the jumping ability from Morrowind made possible (no more roof-hopping across town, which was also a thrill.)
Amusingly, it's possible in the early game to gain items that will allow you to survive the fall from using the scrolls of Icarian Flight. This then allows you to Speed Run the game in about 8 minutes instead of the usual 40 hours.
... Assuming, of course, that you also know where a bunch of people to kill for plot-relevant teleport scrolls live, and are able to exploit a glitch that boosts your stats enough to fight the endboss at level one. It's still an awesome achievement of gameplay, though.
In Killer7, this is a supernatural ability of Coyote Smith, one of the Killer7 assassins.
Unreal, Unreal Tournament and Unreal Tournament III have AntiGrav Boots which will enhance your next three jumps, allowing you to catapult yourself to the top of a level. While walking, you won't boot-jump, just regular-jump.
Banjo-Tooie has the Springy Step Shoes, and also the Leg Spring ability learned by Kazooie solo.
Implemented poorly like everything else in Red Ninja End Of Honor. You have a high jump scroll that makes you do...high jumps. It however does not specify that you can actually jump anywhere except straight up, and they mean "high" as in "comparatively higher than your normal jump". Considering the titular character can simply use her grappling hook to launch her onto rooftops, one wonders why this thing is even in the game at all...
The Pokedex entry for Blaziken in Pokémon Ruby and Sapphire says that it can "easily clear a thirty-story building in one leap". Wow. Unfortunately, in the actual games (with the exception of Sky Uppercut, which can hit Pokémon whilst they're using Fly), the ability is never actually used.
Doduo and its evolution Dodrio are flightless birds, but can learn Fly. One of the only possible explanations is that it can jump really well.
The Gen IV Pokedex notes that a sufficiently powerful Magikarp can Splash over a mountain.. .and that it's still worthless.
Superman can jump really, really high in the NES Superman game. The perfectly ordinary Clark Kent can jump just as high.
Jumping as Superman in that particular NES game, if you were right next to a building, would trigger a "Leap tall buildings in a single bound" cutscene and put you on a different part of the city
In Ultimate Spider-Man, Venom cannot webswing. However, he doesn't have to since the button for webswinging while playing as Spider-Man is changed to a super jump that easily lets Venom clear a ten story building and a couple city blocks.
Alex Mercer from Prototype can jump incredibly well, especially with the ability maxed out and fully charged. It naturally leads to Roof Hopping given the city environs.
James Heller from Prototype 2 is able to jump even higher.
Canabalt is all about jumping higher then physically possible.
Both averted and played straight in Deus Ex. By default J.C. can't even jump as high as a normal human being could, but with the right nanotech implant and upgrades he can jump absurdly high.
Sonic had always had the ability to jump in great height and distance. It's included with his Super Speed.
In BlazBlue, this is surprisingly performed by resident Mighty Glacier Iron Tager. In his Genesic Emerald Tager Buster Distortion Drive, he throws the victim into the air at least five times his considerable height, then jumps after him/her/it without apparent assistance and catches the victim for a Meteor Move. It hurts as much as you'd think it does.
Tager's Astral Heat, which involves him jumping into SPESS and pile-driving them.
Zangief from the Street Fighter games can jump several times his height during a Final Atomic Buster, with the crowning moment of glory/nonsense being when he jumps into friggin' orbit in EX 2.
Ditto for Low G Man who, when fully powered-up, can jump up to 20 times his own height.
In the first Dark Cloud, every single human in Matataki Village and Seda have this ability, though it's usually just vertical. Goro is the best at it until he suffers from the Law of NPC Relativity upon joining your party. Monica Raybrandt in the second combines the horizontal and vertical aspects. Gaspard isn't quite as impressive, but flipping over Monica could qualify.
The Agent in Crackdown initially can't jump higher than a normal person, but can max out his agility to leap fifty feet in the air. At that point driving a car to get around the city is optional as the Agent can leap across rooftops.
BloodRayne can jump insanely high (maybe ten stories or so) and land lightly on her feet, probably because she's a half-vampire. Oddly, most of the first game is set indoors, so the crazy jumping powers aren't usually necessary. They do make it convenient to get around, though.
In Legend Of Success Joe, the ruffian and Harimao can jump high enough to clear the screen. Yet the player has no jumping ability, which is odd for a video game.
Tales of Symphonia gives all characters a jump in battle mode that easily lets them leap over grown men's heads. This makes a certain amount of sense for the athletic fighters among the cast; not so much for purportedly frail magicians like Genis. Even the anime adaptation, not bound by the game engine, has Genis avoid a monster's attack with a skillful backflip.
Judith from Tales of Vesperia also invokes this trope. Her entire battle style is aerial, she can easily jump as high as the battlefield reaches as well as can stay in midair for ridiculous amounts of time.
This is Asura's usual method of jumping to really high distances.
In addition to its original effect of Super Speed, the Bunny Hood item in the Super Smash Bros. series greatly increasing the jumping ability of its wearer. In the case of characters like Luigi and Falco who already jump extremely high as it is, it'll make them go flying off the top of the screen on a small level (Which fortunately isn't fatal).
Omnipresent in Metal Gear Rising: Revengeance. Even generic mooks can jump their own height or more and custom cyborgs like Raiden and the Winds of Destruction can do much better.
Artorias in the DLC for Dark Souls is capable of launching himself across the arena in which you fight him. Bonus points for seemingly hanging in the air for a split second after the jump before rocketing toward you sword first.
XCOM: Enemy Unknown: Easily done by the Thin Men and Chryssalids. Enemy Within adds your genetically-enhanced troopers who can do the same.
The cyberjump ability in E.Ψ.Ǝ.: Divine Cybermancy ramps up your prosthetic legs' muscles, allowing you to vault several meters into the air. Leveling up the agility stat and buying improved cyberlegs allows you to jump several stories into the air, useful for Goomba Stomping enemies.
All three outsiders in Project 0 have had at least one. Owen is the only one without a cool landing to go with it.
In The Adventures of Dr. McNinja, Bruce Lee leaps to the Moon from the Earth and becomes a permanent guest at Dracula's moon base. After meeting with him to learn the technique, Doc manages a similar feat.
Sailor Ranko, which actually shows Ranma jumping over a tall building when he tests out his new Senshi abilitys.
And it shows up again in a later episode, where Jack beats the Scotsman at jumping (among other feats).
He-Man and the Masters of the Universe (1983): One such scene in one of the animated series has He-Man and Battle Cat leaping over a lake of lava and landing in the coolest way possible. If you were to have seen it, you'd probably wonder why he even keeps Battle Cat around.
And, of course, the inevitable Avatar: The Last Airbender example: Justified for the protagonist, as airbenders are able to leap high and far distances by conjuring gusts of wind and cushions of air. Earthbenders are similarly able to catapult themselves into the air and soften the earth for safe landings.
As noticed by many fans, the justification is pretty much out the window for Fire Nation characters, who are portrayed to have the second biggest leaps in the series for no apparent reason. In "The Boiling Rock", Azula demonstrates a technique that can best be described as the firebending equivalent of a rocket jump. The funny thing is that this is still shorter than how high non-bender Ty Lee can jump normally.
Under the influence of Sozin's comet, skilled firebenders can use rocket-feet to fly. This was alluded to as early as "The Southern Air Temple": Aang reasons that the air temples could not have been violated because they're completely inaccessible from the ground...
In Young Justice, Superboy can't fly like Superman and when he realizes this he almost goes into a Heroic BSOD. He can still jump at impressive distances though. Kid Flash even uses the "Leap tall buildings in a single bound" line.
Teen Titans: Red Star is shown doing this. Robin, Red X, and Slade — all Badass Normals — are perfectly capable of performing unassisted jumps that would be completely impossible in Real Life.
In Superfriends, the "Junior Superfriends" Wendy, Marvin, and Wonderdog don't really have any superpowers as we know them. However, Marvin has an ambiguous ability to do "super leaps".
In Skyland, Seijins use their telekinetic powers in a similar fashion.
Star Wars: The Clone Wars: Where to begin? Almost every character appears to have supernatural jumping powers. For the Jedi and Sith, this is justified. (See Star Wars above). But when young Boba Fett manages to jump high enough to kick an enemy a foot or so taller than him in the head, there is no excuse.
This might have been the problem of reusing bits from battles in other seasons. Most likely they simply forgot to check it over with reality.
Cats jump several times their height/length routinely. A mountain lion can jump up to 25 feet. Your average housecat can jump probably 6 or 7 feet high.
Then there's fleas, which can jump many times their height, and grasshoppers and crickets, which have specialized back legs specifically for jumping. And frogs. And kangaroo rats. And real kangaroos. And ...
This is an application of the Square/Cube Law, since the relative jumping strength goes as the square of the size and relative weight goes as the cube; in fact, all else being equal, the actual (not relative) jump height is constant with regard to the scale. In other words, if you made a human (who could jump maybe 2 feet) 5 times bigger, it would only be able to jump 2 feet still, despite being 30 feet tall. Consider that a cat, 1/10 the size of a human, can jump heights/lengths comparable (within a factor of 2) of a human's. Consider that one of those crazy tropical jumping spiders (~1 inch) and your common everyday flea (~1/50? inch) can jump about the same height, which isn't even all that different from the jumping height of a human despite the thousand-fold difference in size. Of course, if all else ISN'T equal (say, the animal is particularly good at jumping due to evolution: kangaroo, cat, etc, or particularly bad: elephant, rhino, hippo), the jump can be several times bigger or smaller.
It also helps that most jumping insects don't use muscle contractions themselves to jump. They compress or extend elastic material in their legs over several seconds. This potential energy is then released all at once and they go flying off like an arrow from a bow.
Powerisers can't quite give you this ability, but they come close, with a maximum jump height of around seven feet for those sufficiently good at using them.
Wuxia films were inspired by real life monks who wear weights all the time while training, making them capable of things that look impossible, but are really just at the high end of normal. See also: professional basketball players and Olympic jumpers.