Flight has always possessed an inherent appeal for humans that most animals don't share.
Millennia of evolution into highly intelligent tool-users and a century of true aviation later, and the appeal still remains — the desire to take to the skies unaided is so basic it's an expected theme in nighttime dreaming.
Much like starburst, flight has quite the rainbow of flavors; to accomplish this feat, characters might ...
One way to recognize a powerful character in Mahou Sensei Negima! is how easily they can get off the ground, and how long they stay off. The fighting tends to get serious when one of the participants takes to the air.
In the Dragon Ball universe, flight is typically the first of the Ki-based martial arts powers the elite fighters learn (well, after "power to massively kick ass") — it appears to be a skill like any other martial art, and anyone can learn it with the proper training.
At the beginning of Dragon Ball, very few characters could actually fly; it was reserved for characters who had to appear impressively powerful such as Tenshinhan/Tien and Chaotzu in their first appearance as antagonists. It was not until Dragon Ball Z was in full swing that characters (after staying months having the same training Goku had before at Kamisama's place) learnt how to use their Ki to fly. The technique is known as "Sky Dancing/Bukujutsu".
There were moments in the original Dragon Ball where characters had to make do and use whatever methods they could to get themselves off the ground. One of the more iconic examples is Goku using a Kamehameha to propel himself upwards and straight through the torso of the airborn Evil King Piccolo. A slightly more comedic example is Goku shooting a Kamehameha with his feet so that he could have his hands free while airborn. An even more comedic example would be Kuririn/Krillin somehow inflating his body like a balloon to keep himself in the air after he is knocked out of the fighting arena. This one-off joke power is not seen again, nor is the Feet Kamehameha.
The Flying Nimbus from Dragon Ball. Though you need to have a pure heart to ride it.
It's even Lampshaded when Goten learns to go Super Saiyan before learning to fly; Gohan compares it to 'Learning to run before you learn to crawl." He suggests Goten be called A Super Pedestrian.
The titular character of Magical Girl Lyrical Nanoha has repeatedly described and been described as loving the ability to fly through the air more than anything else. In StrikerS several of the lower level mages who are incapable of Flight have said that their greatest goal is to take to the skies.
While some characters have a Double Jump or use their abilities in a way to stay in the air longer than usual, true flight is notably rare in One Piece. Only three characters (out of Loads and Loads of Characters) have been shown to have it thus far: "Peregrine Falcon" Pell, Lafitte (one panel in Impel Down shows him with wings while landing) and Marco "the Phoenix".
Mai's magatama rings give her the ability to levitate and fly, though it takes her a few episodes after obtaining them to stop skidding after she lands.
Natsuki's CHILD, Duran, also has a flight mode, though it isn't as frequently used.
Several characters in Soul Eater can fly, by way of brooms, familiars, hover boards, and adapted Weapons. The only two shown to do so under their own power are Asura and Shinigami. Shinigami's ability to fly suggests that Kid will eventually learn how to as well.
Orche from March Story gained this ability after getting possessed, which he uses to take girls dancing in the sky... and then drop them onto spikes.
Despite the prevalence of crazy supernatural abilities in Naruto, only a handful of ninja can actually fly; all three Tsuchikages can control gravity to give themselves and anyone else they touch flight, Fuu does it by manifesting the wings of the demon beetle sealed inside of her, and Sai, Deidara, and Gaara can instantly create flying platforms made respectively of ink, clay, and sand.
While originally possessing only the ability to "leap tall buildings In a Single Bound", Superman later gained the power to fly. The comics moved from showing his leaps to just showing him taking off, landing, or in mid-jump; the Fleischer Studios animators interpreted this as flight. They made a real effort to portray it as super-jumping for much of the run; if you watch the cartoons in order, you'll see a gradual change towards flight. This change was back-propagated into the comics.
In the Marvel Universe, Namor the Sub-Mariner, his cousin Namora, and her daughter Namorita all possess wings...on their feet (echoing the mythological example of the Greco-Roman god Hermes/Mercury).
The Human Torch of the Fantastic Four was originally explained as being "lighter than air" due to his fiery nature, later on it's established that he uses his flames themselves a form of propulsion and lift.
Kitty Pryde of the X-Men can, while insubstantial, walk on air as if traversing an invisible staircase.
Also from Marvel, The Mighty Thor can fly by throwing his mighty hammer, Mjolnir, and simply not letting go. At least originally; modern writers have apparently decided this was too silly. When Thor has to remain stationary in midair, his preferred method is spinning his hammer around his head and hover like a helicopter.
Prince Vultan (and the other Hawkmen) of Flash Gordon are Winged Humanoids whose culture is based entirely on flight — their kingdom is a large flying castle. They dress (and act) like stereotypical Vikings in the 1980s movie.
Most of the Front Liners could fly in No Hero. Controller said that it consumes a lot of calories so they have to eat a lot. Also, landing is very tricky and she had broke her knee the first time she tried to land.
Orient Men can fly, and that's pretty much his sole superpower. He once met a doctor who was certain that Orient Men is just a madman who is deluded that he can fly. When Orient Men indeed flew away, the doctor concluded that it's a particularly severe delusion.
Valiant Comics' Zephyr is a somewhat overweight young woman who can fly. And that's it. She insists on dressing in brightly-colored tights and a cape like a traditional superhero, in the Darker and Edgier Deconstruction universe.
John has been transformed permanently into a Winged Humanoid (not human, as he finds out to his sorrow later). He can't take off from the ground and requires a boost of some sort if he doesn't have a cliff to jump off. When flying, he cannot carry anything much bulkier than a megaphone, explicitly pointing out that he can't even fetch groceries.
The various incarnations of Mechagodzilla are typically equipped with rocket-powered flight (either innately or via an add-on unit). Notoriously, Godzilla himself also used his atomic breath like a rocket in Godzilla vs. the Smog Monster. No, really.
In the animated film The Flight of Dragons, dragons fly by buoyancy; they keep gemstones in their craws, use them to grind limestone, the limestone reacts with stomach acid to produce hydrogen, and bingo, flight and fire breathing as a two-for-one.
Notably, this concept is three kinds of stupid: 1) it takes massive volumes of hydrogen to provide lift, 2) it's extremely explosive (one dragon breathes on the "air sack" of the other and you get the Hindenburg), and 3) limestone plus acid equals carbon dioxide... which is going in exactly the wrong direction for both the powers quoted.
In the Italian B-movie L'Uomo puma (known to MST 3 K fans as "The Pumaman"), the main character has all of his powers based on puma abilities — including the ability to "leap" great distances (as a visual effect, indistinguishable from stock superhero flight). This delights Mike and the 'bots no end ("Are pumas known for their ability to fly?"). Adding to the comedy is the obvious blue screen flying effects along with the actor being suspended by wires, along with unstable camera shots, making it seem as if The Pumaman is not only floundering around, waving his limbs wildly, but is flying in odd directions (i.e. sideways).
In Man of Steel, Clark can break the sound barrier and engage in aerial combat.
If the eponymous villain in Warlock performs a certain spell for which he needs to kill and harvest a child, he can fly through the air at his own discretion.
Early literary example: J.M. Barrie's Peter Pan. Peter can fly by himself, and shares the power with his companions via fairy dust. In later adaptations Peter's flight has an unusual weakness: you have to think happy thoughts to fly. This means that sad people can't fly until they change their attitude. This was even deconstructed with Captain Hook in a Peter Pan live action, getting pixie dust and flying because getting to fight Peter on a even playing field makes him very happy. (This weakness, like Neverland being "the second star to the right", was something Peter only said because he's incapable of telling the Darling children "I don't know" when they ask him questions, instead making things up. Later movies took both of these and ran with it.)
Throughout Harry Potter, flight via broomstick, car, and motorbike (and, it was implied, magic carpet) is commonplace. Somehow never explained in the last book,Voldemort and Snape both gain the ability to fly without any other apparatus. It's implied that Voldemort invented an unaided flight spell, a sign of his magical genius.
Also depending on your interpretation at the start of book 1, Harry's accidental magic of "jumping and appearing on the top of the school" is either flight or Apparation, but due to Lily Potter's accidental Hovering in Snape's memories it is more likely flight.
Winged centaurs in Xanth have the talent of making things lighter by flicking them with their tails. In order to fly, they flick their own butts a few times and then take off. This also justifies the ability to carry immense weights, because anything they have to carry they simply make lighter. An added benefit is that if you fall off of the winged centaur's back mid-flight, you'll float to the ground as if you had a parachute. However, if you've just disembarked and it's windy, you could have trouble.
Star Wars Expanded Universe: Force Flight falls under the "telekinetic" variant of the power, but it is very difficult to pull off successfully, let alone for long periods of time (it tires one out easily due to the sheer amount of concentration and energy required); not even the Skywalkers (contrary to the name) use it with any frequency.
In Victoria Forester's The Girl Who Could Fly, as the title said. Piper first flew when she rolled off the table while her mother was changing her diaper. Since she was born very late to a woman who thought herself barren, the mother's first thought is that that's the sort of thing you expect when doing things the way they shouldn't be done.
Live Action TV
In Smallville, one of the major criticisms is directed toward Clark's "no tights, no flights" rule, although he has flown in Crusadeand in the finale. Warrior lampshades this by having a boy receive superpowers including flight, which he didn't know before. He immediately goes "Holy crap! I can fly!"
In The Flying Cestmir, Cestmir is transported to a plannet of plants and gains six magical seeds which he grows into flowers. Smelling their scent gives people super abilities and skills for a certain period of time. One of the flower causes that Cestmir and others can suddenly fly.
Not surprisingly, this is commonly ascribed to gods, angels, demons, witches, etc.
Several Greek gods and monsters can fly thanks to the bird wings growing from their backs, and Hermes gets to fly solely because of winged sandals. Daedalus and Icarus flew using mechanical wings.
In the futuristic world of Bally's Xenon, everyone flies around simply because they can.
Flight is one of the special abilities that many creatures possess in Magic: The Gathering. Only other flying creatures, or creatures with the special ability "Reach", can block fliers. While there are many many spells and creatures that can counter flight, it's still a powerful ability that should not be overlooked. Especially since some of the most powerful creatures in the game such as dragons, angels, and vampires all possess it.
In BIONICLE, Toa Lewa possesses the Mask of Levitation and Toa Nuparu uses the Mask of Flight. The two are related, but different — rather like a hot air balloon and an aeroplane respectively. Additionally, both Toa Lewa and Toa Matau have swords that can be used as wings. As Toa of Air, they use their control over the winds to aid them in their flight.
Mario seems to win a new way of flying with every console generation (except the Gamecube): The Tanooki suit, Magic Ballons, the Feather cape, Wing cap, and lately a more conventional Up, Up and Away! method of flying using red star's power.
The Rocket Nozzle attachment for FLUDD in Super Mario Sunshine gives him the power to fly straight upward.
His friend/steed Yoshi could fly in Super Mario World as well, but only for a limited time when holding a blue koopa shell (or any koopa shell if the Yoshi was blue). Later games mellowed it down to a limited ability to flutter in the air for a few seconds. In Super Smash Bros. Brawl however, his Final Smash lets him grow wingsand spew fireballs.
Miles "Tails" Prower flies, very fast, too. Guess what he uses.
Cream the Rabbit is also capable of flight to a limited extent, using her giant floppy ears (as is her Chao partner Cheese, who presumably absorbed the power from her). Rouge the Bat more conventionally uses her wings, though whether this is flight or just gliding varies between games.
In Sonic Colors, the Orange Wisp allows Sonic to fly straight up into the air, destroying enemies and obstacles along the way.
Charmy Bee. The bee who's flying almost every second he's on screen.
Ditto with the eponymous character of Conkers Bad Fur Day. Although it's more like a double jump due to it's short duration.
Flight is one of the Pool Powers in City of Heroes that can be taken in addition to the main powersets, one of four 'travel powers' (the others being Super Speed, Leaping and Teleportation). It's notable among the powers for being technically the slowest, but providing full 3D movement and being very easy to use. And oddly enough, the pool includes a melee attack specifically for use against flyers. The Peacebringer Epic Archetype gets Flight for free. Several popular Temporary Powers are flight-capable jetpacks.
Pilotwings and Pilotwings 64 were all about this, using various vehicles to fly around islands and complete challenges. The ultimate prize was the Birdman outfit, which allowed you to fly around the islands without crashing or needing fuel.
Get this — Rayman can fly by making a helicopter out of his hair. To avoid Game Breaking it's usually just depicted as gliding during most gameplay segments, but there are some instances while using special items or level-specific powers where he can just flat-out fly.
In a couple of the Devil May Cry games Dante's Devil Trigger can be upgraded with the power of flight.
In the Heroes of Might and Magic series, flight is incredibly useful. In battle units that can fly avoid all obstacles on the field including siege walls; not something to be taken lightly. And some of the strongest units in the games like dragons and angels all share this power. On the adventure map it's a total Game Breaker since the hero can fly over water, mountains, and garrisons. The spells and artifacts that grant flight are usually disabled in campaign scenarios for this reason.
The first boss of Bug!, a giant snail. How does such a thing fly? It goes into its shell, a helicopter rotor comes out, then it takes off. And then it'll start dropping bombs all over the place (or trying to crush Bug)!
Several characters in El Goonish Shive have some form of flight. Nanase has a spell that allows her to fly, as does Elliot (but the spell turns him into a comic book superheroine rather than simply allowing him to fly), and Grace can use her telekinesis. Two villains have also been capable of magical flight.
Jack of Gunnerkrigg Court recently displayed the ability to fly. However, unlike most examples on this page, it is treated as something special and even borderline unbelievable by several characters despite the fact that many other magical abilities have been seen.
In The Order of the Stick the Empress of Blood can fly. She's a dragon, so this would be expected. But she's also an Adipose Rex. The strip that demonstrated her flying ability was titled "Maybe She Swallowed a Zeppelin". Vaarsuvius can fly - if s/he casts the (presumably Overland) Flight spell, of course, which it seems s/he, as a high-level wizard, has made a habit of casting when the day starts.
Every one of the listed ways of flight has been adopted by at least one of the characters in the Whateley Universe. Of course, since it's at the Super Hero School Whateley Academy which has nearly 600 students plus a host of superpowered teachers, it's inevitable that a lot of people there can fly or have figured out how to fake it. One way not mentioned in the list at the top of the page: one girl with magical powers has given her horse wings so she can fly on the horse's back (her horse also magically communicates with her).
In the original Transformers series, the power of Flight was one of the defining characteristics between Autobots and Deceptions — all Decepticons could fly in their robot form, but only the few Autobots with air or space transformations could do so (plus Sideswipe, who was equipped with a rocketpack, and Tracks, whose car altmode had wings). The Dinobots could fly in their robot modes (Swoop in either mode). No reason given for why, but it was awesome.
This leads to a brief Let's You and Him Fight situation in Transformers Animated when the Earth Autobots meet Jetstorm and Jetfire, two Autobots on Sentinel's team who have been upgraded with flight capability based on Starscream's specs. The Earth Autobots briefly mistake the two for Decepticons and attack them because, to the best of their knowledge, only Decepticons can fly. In the Grand Finale, Rachet builds a jetpack for Optimus so he can fight Megatron on a more even footing.
Static from Static Shock flies by magnetically levitating any handy metal platform. In early episodes he would use a nearby garbage pail lid or manhole cover, in later episodes he carried a folding metal disc in his pocket.
Jade from Jackie Chan Adventures would combine the power of the Rooster (levitation) and the Rabbit(speed) talismans to give herself flight.
On The Fairly Oddparents, fairies, pixies, anti-fairies, and genies can fly. Oddly, though all of them except genies have wings, they never seem to use them to fly. It's also one of the Crimson Chin's powers, and Crash Nebula can use a jet pack.
The Furlings from Once Upon a Forest build an aircraft using Bamboo Technology called "The Flapper Wingamathing" so that they can retrieve a herb growing on a tall cliff-side for their comatose friend.
Of the Teen Titans, Starfire is a Flying Brick, Raven is telekinetic, and Beast Boy transforms into birds. Robin and Cyborg have to make do with single-episode glider capes and rockets strapped to their backs, respectively. Usually Robin and Cyborg are in the care of their flight-capable companions during the stints when they have need.
The eponymous creatures of Gargoyles possess wings, but as they explain to Eliza, they are not capable of true flight, instead gliding on warm air currents (though this doesn't prevent Brooklyn from flapping his wings a couple times to try to stay aloft while carrying and unconscious Lexington).