A weird example of video game Jump Physics, the Double Jump is the ability to jump while you're still airborne from your first jump, thus gaining additional height or distance. Exactly how this is supposed to work is unclear; games that justify it through Rocket Boots, etc. are the rare exception. Even more rare are games that justify why you can't repeat the action indefinitely to achieve Video Game Flight.
In most cases, its purpose is indistinguishable from simply letting the player jump higher, though it is occasionally useful for dodging certain ground attacks. Sometimes the second jump must be initiated at the apex of the first jump; other times the player can, rather absurdly, jump again while on the downward trajectory of his previous jump. Some games have obstacles that can only be passed by jumping under them, then double-jumping to safety on the other side.
A staple of platform games, including metroidvanias, and fighting games. Frequently, the double jump is a Power-Up learned later in the game, alongside the Wall Jump. In a later generation of games, double jumps weren't considered cool enough anymore, giving rise to characters with a triple jump. Indeed, this has led many games (especially later games) to have double jumping as just standard issue, with no reason or logic; for these games, it's just how jumping works.
Visually speaking, if there is a visual effect at all, chances are it will be a "ripples on water" effect.
Action Adventure Games
Most Castlevania games starting with Castlevania: Symphony of the Night have an item that allows the use of double-jumping. There is often another item that allows for infinite long leaps straight upwards (sometimes draining MP).
Alucard from Symphony of the Night is perhaps the only character who has his double jump explained in some way: while most other protagonists simply jump a second time, Alucard's cape briefly transforms into a pair of wings and flaps to hoist him up.
Soma in Dawn of Sorrow does a flip in the middle of his jump, not that that justifies anything.
In Castlevania: Portrait of Ruin, Charlotte double jumps by briefly summoning and riding a broomstick. Why this doesn't enable her to just fly remains unknown. Her partner Jonathan just jumps again in the air for no readily explained reason.
An even earlier example in the Castlevania series is Maria Renard in Rondo Of Blood, the prequel to Symphony of the Night. Richter did not have this ability, but Maria did, making her perhaps the first Castlevania character to possess a double jump.
Most of them use "Relics" to accomplish double jumps, and some (Stone of Flight) make more sense then others (Ordinary Rock. Seriously, in Castlevania, an Ordinary Rock lets you defy the laws of physics).
The Ordinary Rock was originally SotN's classic Leap Stone. Just one odd translation and it becomes a universe where everybody is literally tripping over magical, blue gemstones only to catch themselves in midair thanks to those very same rocks.
An inherent ability of all lightsaber-wielding characters in LEGO Star Wars. Of course, it's the massive single jumps that are mostly used for unlocking secrets, but still. Somewhat justified for Jedi & Sith as being a Force power, but no explanation is given for how General Grevious pulls it off... also, for some reason, Jar-Jar Binks can do it too.
In the level builder of LEGO Indiana Jones, the engineer character, and the other ones that you use to build the level, can infinite jump until they hit the roof of the level — and one of them is for putting down baseplates, so he can infinite jump while holding the floor.
You get this in An Untitled Story as the earliest ability. Later on, you'll encounter double-jump rechargers, floating power-ups that let you jump one more time in the air.
In Brave Fencer Musashi once you obtain the Legendary Belt, you gain the ability to double jump which is required to jump over wide gaps later in the game.
Devil May Cry (the first game) explained this as being one of Dante's demonic powers. The second game kept the "Air Hike" as one of his standard abilities, probably because the sprawling environments made it so useful, though the later games returned to needing a purchase.
It's worth noting that the games, despite their normally loose interpretation of physics, actually have Double Jumps that make more sense than most. When you use it, Dante momentarily makes a magic platform appear beneath his feet, off which he jumps.
It's also worth noting that if he's close to an enemy or wall and tries to double jump, whether he has the move or not, he'll use the enemy/wall to double jump. One secret mission in 3 requires you to stay in the air for twenty seconds. This involved double jumping off enemies, walls, your ability, and almost always spamming your fire-pistols-to-fall-slower ability.
Bayonetta temporarily forms butterfly wings when she double jumps, Justified as she's a witch.
Even more justified - if you read one of the books in the Records section of the menu, you learn that she made a deal with the demon Madame Butterfly for this power. When Bayonetta is standing in light, her shadow has butterfly wings to signify this deal.
Of course, The Force Unleashed, where the Secret Apprentice gets both a double jump and the air dash; some parts of the game (at least on PS3/Xbox 360) require that you use both-though again, he is a powerful Force-Sensitive.
Gotcha Force uses many different types for different characters. Most can triple- or quadruple-jump, and have infinite air-dashes. Machine, Girl, and Tank Borgs have a boost meter that's used for both jumping and air-dashing; they can't jump normally. Wing and Angel Borgs obviously have infinite jumps, but they're all incredibly small and not very useful for gaining height. Air and Fortress Borgs never jump, since they're always flying.
In Shinobi III, the player character, Joe Musashi, has this ability.
Seig can do this in Chaos Legion after acquiring a power up from his Flawed legion.
All characters in Super Smash Bros. can double jump. Most characters also have a special attack that can be used as a third jump, while still others can can jump several more times because they can fly.
Meta Knight can be particularly annoying to fight against, as three of his special attacks give him lift, can jump up to 5 times, and can glide.
A standard ability in Guilty Gear. Chipp, being a Ninja, can triple-jump. Even the Mighty Glacier Potemkin, who has so much muscle that he weighs 1000 pounds, can double jump. (but he can't run.)
Sadly, his spiritual successor Iron Tager, can't do it.
A tenet of the Gamecube game Custom Robo; it appears in different forms in each group of mecha types. They do have jets, being mecha, though.
Double (or more)-jumps include one (for Mighty Glaciers) or more (Mario) sideways air-jumps, 'stealth' jumps (appearing like short warps), small vertical jumps or a long-distance glide (for the two arial-specialist groups), and a weird kinda floating-rolling one.
All characters in Eternal Fighter Zero can double jump. It makes sense for characters like Kanna, who just flaps her wings again, but for the rest of the cast...
In the third Ranma ½ fighting game for the Super Famicom, Super Battle, Female Ranma and Shampoo can double-jump. But only if their starting jump was a forward or backwards somersault, rather than straight up.
All characters in Dissidia: Final Fantasy can double jump initially, except Bartz and Zidane, who triple jump. Everyone can learn Jump Times Boost++, which gives three more jumps. However, Zidane is beyond this - with Jump Times Boost++ and his EX mode he can jump sixteen times in a row! But wait, there's more! If you dodge in the air it resets your mid-air jumps! So Zidane could jump sixteen times, dodge, then jump another fifteen times without ever touching the ground.
In Touhou Scarlet Weather Rhapsody, each character's double jump is actually a flight command, which consumes some of your spirit orbs to execute.
Since jumping is more a feature of the Street Fighter series than Tekken, most of the Tekken side gained increased jumping ability in Street Fighter X Tekken. Lili is the only one however to gain double jump, though it's executed on her way down instead of at the apex of her jump.
M.U.G.E.N allows you to set the number of jumps a character can perform in midair. Cue fighters hovering over the stage for a full minute and duking it out above the camera's view.
Divekick has two characters that can double jump - resident troll Stream must jump twice before he can even follow up with a kick, while the Final Boss, S-Kill can either kick or dive again after emerging from his teleports.
The Scout class in Team Fortress 2. Double-jumping is actually one of the class's greatest tactical advantages, since it allows Scout players to reach otherwise inaccessible areas and surprise their enemies. He can achieve a third jump with with the Recoil Boost of the unlockable Force-A-Nature or by holding the also unlockable Atomizer (taking 10 damage per jump). He can even do a quadruple jump if you have both.
Unreal Tournament 2004 has double jumping active by default in deathmatch mode. There's even a mutator that enables quad jump.
This could be further augmented with the Low Gravity mutator. It's possible to soar across half of the enormous Onslaught maps with these on, leaping from vehicle to vehicle like Neo. Unfortunately, Low Gravity is disabled in Unreal Tournament III on Warfare maps.
Later on in Half-Life 1 right before you go to Xen you obtain a upgrade called the Long Jump Module, which is basically a miniature jet pack that fires for a brief second and acts like a double jump. The second jump barely gains any height, and just sends you flying a further distance.
Sniper Path Of Vengeance has a bug where trying to momentarily duck while at the apex of a jump (holding the jump key) results in a double jump - an infinite jump to be exact.
Hack and Slash
In the Samurai Warriors games the ninja characters could double jump, but subverted in the Warriors Orochi series where all Speed-type characters can Air Dash but not double jump straight up.
Kratos in God of War actually starts with this (in the move list it's called "Icarus Lift"). His jumping ability never improves during the game, leaving one to wonder why they didn't just give him a higher single jump to begin with.
It's implied that the double jump is a property of his Blades of Chaos/Athena. The double jump is listed in the same place as the combos for those weapons., including a combo that lets you jump fifteen feet straight up.
Raikoh from Otogi Myth Of Demons can do this, and in the Sequel it's the standard, with some characters being able to jump less or more, and one character who can jump infinitely, though at least that last one has an excuse, since he's a magic floating tree.
Momiji in the Ninja Gaiden series. She even can perform an Ultimate Attack from the second jump, which makes her very versatile.
Surprisingly for a series that's used nearly every other jumping trope, Mario has almost never had a double jump. He had a spin that gave him a bit of hang-time in Super Mario Galaxy and its sequel and New Super Mario Bros. Wii, but that's about it.
Spaz in Jazz Jackrabbit 2. Which enables him to reach areas his brother can't.
In the Metroid series Samus has the Space Jump. Which isn't a Double Jump, it's an Infinite Jump. On the other hand, it only works while she's doing her "roll jump"; a straight jump upwards won't allow it to trigger, and if she fires any weapon in the middle of a jump, or straightens up, she plummets back down.
Except in the Prime games, where it is a Double Jump. The Screw Attack is used for longer distances instead.
The Metroid series is also one of the few where this is justified, as Samus's power suit is equipped with boosters, and once you get the gravity suit, some type of antigrav device. There's speculation that the bulky gizmo on her back is involved. Note too that Samus can't get away with the cheap "double-jump before landing" trick to avoid the stun a long fall delivers in the Prime games — if you wait too long, you can't Space Jump.
Her appearance in the aforementioned Super Smash Bros. series (specifically brawl) confirms that, yes, that thing on her back is indeed a small booster used for double jumps.
Echoes also shows her using it as a jetpack, and Hunters explains that she has a "jump booster" that lets her jump in mid-air.
The Lost Vikings 2 and Xain'd Sleena are two of the rare exceptions that use rocket shoes for the second jump.
Banjo-Kazooie explains it by having Kazooie come out and flap her wings a bit, which gains you a little height. The Pack Whack move in Banjo-Tooie lets Banjo solo do a Double Jump.
However, the Pack Whack won't stop you from hurting yourself when jumping from a high place - do a suicide jump, hit the button exactly before you hit the ground, and Mr. Bear would still smash into the ground like a boulder.
In Sonic The Hedgehog 3, Sonic gains the ability to increase the area that his Spin Attack effects by pressing jump again while jumping. The three shields augment this: the Electric Shield allows him to actually Double Jump, the Fire Shield lets him charge forwards while in midair and the Water Shield lets him execute the equivalent of a Ground Pound. In Sonic Adventure, this is taken a step further with the homing attack, a very useful double jump that lets Sonic lock-on and attack the nearest enemy. Finally, double jumps are the way you get Tails to start flying and Knuckles to start gliding.
Hyper-Sonic also has a double-jump, with the added bonus of killing any one-hit enemy who happens to be on screen.
In Sonic R, double-jumping is Sonic's special ability.
In Sonic the Hedgehog (2006), the titular hedgehog can buy a gem which makes him tiny. While he's like this, Sonic cannot stop moving, but he has an infinite jump, too.
In the recent 2D Sonic platformers, including Sonic Advance 2, 3 and both Sonic Rush games, both Sonic and Blaze can perform a double jump, but only after being launched from a spring or similar device.
Blaze's animation somewhat justifies her double jump, as she appears to summon flames and uses them as jets. Yes, her double jump is bigger than Sonic's.
In Sonic Colors, Sonic has a double jump and homing attack as his default abilities in the air, while in the water, he can double jump infinitely. Which makes this the first time Sonic's ever been able enter water without sinking like a rock or dying instantly.
In the Super Famicom/GBA game Mega Man & Bass, Bass has this as a default ability in, and its little-known not-made-by-Capcom sequel of the same name on the Wonder Swan, while Zero can gain the ability in the X and Zero series games. In X8, it has become part of his default abilities.
Also, starting with X2, X gains the ability to use various air control abilities, including the ability to dash in mid-air. In X3, he can dash straight up. In X4, he loses the straight-up dash, and instead gets the ability to hover. This continued until X7, where X can now glide (which is as useless as it sounds), and X8, where he gains the ability to do a smash jump, but no double jump (that's for Zero only).
Mega Man Network Transmission has a Battle Chip that allows you to jump in midair. But like all other Battle Chips, you were limited in the number of times you could use it per level.
Psychonauts justifies this as one of the protagonist's psychic powers — you can even see him materialize a temporary midair ball to jump off of.
This is your only real useful ability in I Wanna Be the Guy. You can also jump out of a fall, which you need to do in some instances.
Klonoa has an interesting variation: the title character can only double-jump when holding an enemy, and the enemy is dropped on the second jump. That is to say, he basically jumps off them. A for effort, at least...
One of the Animal Helpers in Kirby's Dream Land 3, a cat named Nago, is capable of performing a triple-jump.
Of course Kirby can jump indefinitely in his earlier games. He lost this ability in Kirby 64, where he was limited to about ten mid-air jumps.
Vectorman has the Double Jump ability, and that is explained by his awesome jet boosters on his feet. They're also a handy way to kill off enemies too.
To give you just an idea of how "handy" they are at killing enemies, if done right you can one-shot the last boss with them.
The Jak and Daxter series has Jak simply thrust his legs down as if he were litterally jumping off of thin air. Daxter could do this too in his Gaiden Game... so maybe this is just something all the people in the Jak 'verse can do.
Ratchet of Ratchet & Clank can do a salto in midair that is soon upgraded to include gliding afterwards (Clank helps with propellers/rocket engines).
In Secret Agent Clank, Clank can double-jump and glide with the use of jet boots.
The Fairly Oddparents video game Shadow Showdown actually Lampshades this trope: "Double Jump. That's right, forget everything you know about the laws of physics and jump again in mid-air."
The first Oddparents game has Cosmo mention that double jumps "give you twice the height and only two-thirds the calories!"
The double jump in Prince of Persia (2008) is, interestingly enough, not actually a double-jump, nor can it be used at any time. If the player jumps toward a platform/column/beam/whatever that is out of the Prince's own abnormally large jump range, the screen begins to turn black and white telling the player they're about to fall. Hitting Elika's command button here causes her to use her magic powers to throw the Prince another jump length - but one's all you get.
In The Legend of Spyro series Spyro flaps his wings to achieve the effect. It even justifies why he doesn't simply fly all the time: He doesn't land well. In the third game, you finally do have free-flight.
Viewtiful Joe can do it as long as he's powered up and in costume.
The first game's unlockable characters have variant abilities: Silvia's jumps can reach higher than Joe's; Alastor mimics Dante's Air Hike while unpowered and can float after a double jump while powered; Blue has no double jump, but instead has a very high single jump plus floating.
La-Mulana lets you Double Jump after you obtain the Feather.
The Donkey Kong Country series has a quirk where you can jump from a roll even if you rolled off the side of the platform and are in midair. Doing this is in fact required to reach some of the bonus areas and items needed for 100% Completion, and Cranky Kong occasionally lampshades this trope in his rants.
Browny is the only character in Contra Hard Corps that can double-jump, via use of a jetpack boost. This makes up for his somewhat shorter regular jump.
Kirby has an infinite number of jumps in his games, but it is justified since Kirby can inflate himself like a balloon.
World of Warcraft got a few of these in Cataclysm: anyone playing a Goblin character can jump and then use the Goblin-only rocket boosters to jump again. Warriors and Hunters can use their Heroic Leap and Disengage abilities mid jump as well, which more closely resembles the original trope.
In X-Men Legends, Beast and Nightcrawler can double-jump. In the sequel, Beast is no longer playable and Nightcrawler has somehow lost the ability (pressing the jump button twice makes him teleport instead), but Toad now offers it.
Amaterasu in Ōkami is capable of this. Considering that by the end of the game she can walk on water, summon lightning, water, ice, and fire, walk up walls, and make plants bloom, a Double Jump is really the least of her abilities.
Considering that she's a goddess...
It's also one of the "God Techniques", which according to the sensei cannot be learned by ordinary people (or wolves).
It should also be noted that after having learned the Holy Eagle technique (double jump) you can later upgrade it to a triple jump.
In Kingdom Hearts: Birth by Sleep Aqua get this as an ability called Doubleflight, and it seems to be explictly magical, because when she does her second jump there's a large burst of magic at her feet, propeling her upwards.
In Kingdom Hearts II, Sora has the Aerial Dodge growth ability, though, unlike most double jumps, it doesn't really make Sora jump that much higher, instead it just gives him more air time.
The Aerial Jump skill in the Tales Series allows you to do this. Also, certain air enabled arts will cause the character to perform an aerial jump as they execute them and if the game's Super Mode is active, they can often to be spammed to ascend all the way to the top of the battlefield or out of sight entirely.
The Dragoon Gauntlets in the Advance and PSP versions of Final Fantasy IV give Kain the Double Jump ability, which simply increases the damage bonus from his Jump attack and changes the attack's animation to show him bouncing off of the target before striking again.
The Wuxia MMO Age of Wushu has "flight" skills, of which double-jumping is the least. It's earned early in the tutorial. Further flight skills include triple-jumping (through spontaneous spinning), running up walls, running across water, and flying in a straight line for a short distance. Mastering effective use of flight skills is essential to PVP combat.
Rurouni Kenshin: Yukishiro Enishi outjumps Kenshin in their final duel using this technique (and there's an attempt to justify it in terms of real world physics, but the explanation doesn't really make sense).
Users of the One Piece martial art Rokushiki are able to do this at will. The technique is called "Geppou", which translates to "Moon Walk" or "Moon Step." Users of this technique are able to perform it as many times as they please while in the air.
Basically, the way Geppou works is that the user kicks the air with their feet so hard in mid-air that it propels them in the direction they kicked.
Sanji eventually masters this move, calling it "Sky Walk."
Cloud pulls off an assisted version in Final Fantasy VII: Advent Children, in which nearly every party member from the original game (including Aeris) takes it in turns to leap up to meet him in mid-air before throwing him even higher. By this point in the movie the laws of physics have pretty much given up and are sulking in the corner.
The titular character of Naruto could conceivably do this using a shadow clone, but it was Might Guy who executed the first double-jump of the manga. In mid-air he summoned a tortoise and used its back as a springboard.
8-Bit Theater's Thief (after his class change to Ninja) once survived an outrageously long fall by double-jumping just before impact. Dragoon also survived falling off the underside of an island by using his jump attack while in mid-air, though he still needed to home in on a target.