While escaping danger, a character who can fly will never think of the quickest way to avoid a pursuer: fly up. They will just fly very quickly... right in front. Worse yet, they may run instead of fly at all.
This is more frequent if a character is around others who can't fly, as it's the only way to create a real sense of danger. Flying up only occurs when the danger does likewise.
Acrophobia is the fear of heights, the idea being that the only sensible reason for a flying character not to do so is because they're literally afraid of heights (if this is genuinely the case, a Die or Fly situation can snap them out of it). The non-flight variant of this is One-Dimensional Thinking.
Compare 2-D Space and Water Is Air. For literal acrophobic birds, see Ironic Fear.
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Lampshaded in a Japanese ad for Tsubasa ("Wing") Finance: a man is watching a TV show in which a winged angel is being chased by (non-winged) swordsmen, only to give up when he gets cornered in a spot with open sky above him. The man watching the film shouts at the TV, "Why aren't you using your wings!?"
Anime & Manga
In Nagasarete Airantou, a bird being chased realizes that he can fly and the humans can't and promptly goes airborne. He muses over why he didn't think of that earlier when he looks down and remembers that he is acrophobic.
Mew Mint in Tokyo Mew Mew occasionally fell victim to this, but she usually did fly up, probably because the enemies could too. We do, however, have the water-controlling, underwater-breathing porpoise-girl Mew Lettuce, who rarely uses these powers, unless she has no other choice...because she really is afraid of drowning.
In Rozen Maiden: Träumend, when Shinku and Hinaichigo are being pursued by Barasuishou, they fly close to the ground for most of the chase. Yes, it's true that Barasuishou was flying above them at the time, but Barasuishou's main attack was to summon crystal spikes up from the ground, which they had to constantly dodge. Logic dictates that the further away you are from the ground, the less likely you'll be hit by the attack.
In Princess Tutu, Ahiru almost never remembers that she can fly in her duck form, even though it's her natural state. Averted in a couple of occasions, but most of the time, she struggles with climbing, even as a bird.
Ash's Oshawott can't control Aqua Jet because he's afraid of keeping his eyes open while underwater. He manages to overcome it later.
Worse would be Misty's Psyduck, a Water-type platypus that doesn't know how to swim. Likely for the Rule of Funny, as it's implied this specific Psyduck is just that stupid.
In Peter Pan No Bouken, the characters are unable to fly once they reach Neverland, making it that much easier for the writers to put them in danger. The exception is Peter Pan himself, who completely averts this trope by flying all the time.
Played straight with Shippou, who had the ability to transform into things or creatures that could float or fly, but who never escaped danger in such a manner. Of course, he's also a very young child, so he can probably be forgiven for not always thinking in a calm, logical way (even if he was sometimes calmer and more rational than some of the adult characters).
Averted with Sesshoumaru's two-headed dragon-horse. The creature was usually seen walking, but that's only because it was Sesshoumaru's preferred mode of transport (if Sesshoumaru flew, the creature would also fly). However, whenever an attack was levelled at the children Sesshoumaru was protecting, the creature's first instinct was always to dodge upwards and drag the children to safety as high in the air as necessary to stay out of danger.
Image Comics heroine Blacklight has flight powers — and acrophobia.
Justified in the comic strip Peanuts with Woodstock, a literallyAcrophobic Bird. Going too high gave him beakbleeds, among several other flight-related neuroses. He had a hard enough time flying forward. In one Sunday strip, Snoopy questions Woodstock on why it is that birds in the path of moving vehicles will hop around on the ground and not just fly away until the very last possible moment. Woodstock replies with several panels full of his unintelligible speech, to which Snoopy responds "That's the worst excuse I've ever heard!"
U.S. Acres: Wade Duck is also a justified example because he's afraid of everything, flight included.
Guard Duck from Pearls Before Swine never learned to fly. This unfortunately means that he couldn't go with his flying duck girlfriend Maura when she flew away.
One B.C. strip has a character sitting on a rock, looking at a dot in the distance. The object come closer and closer as we see it is a bird walking. Just as the bird passes the human it looks up at him and says "Bursitis". It then walks away.
One Far Side comic titled "Stupid Birds" shows a pair of birds attempting to escape a burning tree using a Bedsheet Ladder.
Films — Animation
Acrophobic Parrot from 38 Parrots is a literal example.
The Land Before Time. Petrie, a young Pteranodon, has not yet learned to fly in the first movie, in which it is a Justified Trope. However, he learns how at the end of the movie, so the sequels don't always make sense. For example, in the ninth film, the group is cut off from their families by a large gorge. Petrie offers to fly over it and get help, but changes his mind after he is nearly burned by a jet of hot air coming out of the gorge. All he would have needed to do is, yes, you guessed it, fly higher. Petrie is mentally about four years old. Whether or not he could fly higher, he's just too scared to try it.
Averted like crazy in Legend Of The Guardians The Owls Of Ga Hoole, and the film deserves some kind of reward for this. Right from the beginning, the protagonist calls the ground "the worst place for an owl", and thereafter, all the avian characters stay in the air or perched up high on cliffs and trees.
Blu from Rio is an orphaned Spix's Macaw who, although he was adopted by a very caring person, was never taught how to fly. He's still a good climber, but takes a long while to get over his fear of actually flying.
Lampshaded in Winnie-the-Pooh. The gang — including Owl — has fallen into a pit and they try to get the anxiety-ridden Piglet to rescue them. Since Piglet is too terrified, Owl flies up to give the little guy a rousing speech, then flies back down into the pit once Piglet's confidence is up. The look on Rabbit's face after all this is priceless.
Films — Live-Action
Averted by The Matrix Reloaded during the burly brawl where Neo is seen trying to escape the large number of Smiths by flying, but they jump at him and stop him.
The 1998 movie version of Godzilla features the eponymous lizard chasing attack helicopters through the streets of New York. The helicopters fly around the streets, being caught one by one, but never pulling up and flying away from it...note Helicopters fly forwards faster than they can climb, due to the added push from the forward momentum. Climbing not only taxes the engine more, but it bleeds off your forward momentum and slows you down. If you are trying to climb straight up, from a stationary position, the ascent is slower still. Bottom line, if you have a 300-foot mutated iguana chasing you at 200 mph, moving forward is the fastest way to put distance between you and him/her (or whatever they determined that thing was). However, this doesn't excuse the fact that they flew that low to begin with; in fact, it would be easier to get a shot on the monster from a high angle where buildings wouldn't give it so much cover.
Averted in Flight of the Navigator when the kid gets into an alien ship with an artificial intelligence. When the kid pleads with the ship to get out of the military base and "fly twenty miles away", the ship decides to do that by going 20 miles straight up.
Inverted in Iron Man 1, as Stark immediately flies straight up upon realizing that Iron Monger is capable of flight... but the latter's flight system is essentially a rocket and doesn't seem capable of much other than straight up. Tony really wasn't trying to escape, though. He was exploting the fact that Iron Monger was a reverse-engineered and massively beefed up version of the Mark I Iron Man armor, complete with design flaws that Tony had corrected with his own Mark III armor.
The title character of Paulie is literally an Acrophobic Bird until he learns to fly.
The Meteor Man. The eponymous superhero uses Superman-like powers to defend his neighborhood from gangsters and doesn't really fly higher than a few feet off the ground because he is scared of heights. Partially justified in that his powers are not one hundred percent reliable.
Stealth features an extremely silly scene where two of the super-stealth fighters are chasing the rogue UCAV through a dangerous canyon; the end result is that one of them crashes, killing the pilot and damaging the other. The third plane? It was flying above the canyon watching this. Apparently, nobody thought the other two planes could just do that too and, since they weren't juking around avoiding the canyon walls, would be going faster by doing so. The UCAV was probably attempting an Aerial Canyon Chase, which is a legitimate but very dangerous tactic.
During the Really Huge Earthquake sequence in 2012, one cluster of protagonists escapes crumbling downtown Los Angeles in a small aircraft that never manages to get above a thousand feet.
In The Mummy Returns, Imhotep reprises his sandstorm trick from the first film with the water from a river instead. The heroes, approaching in a dirigible through the twisting pathways of a canyon, are forced to flee when the water surges up and chases them. Their initial reaction — firing up the booster rockets and outracing the wall of water — is understandable because of the element of surprise, and even with rockets, they could barely keep ahead of the water, so there really was no time to fly up. However, after they've (temporarily) escaped, they hear the water again and just float there, waiting for it to hit them, instead of flying up and out of the canyon where the water can't reach them. Although dirigibles gain altitude only slowly, they could have pointed the rockets downward. In real life, this would probably burst the balloon, but they do it later in the film successfully.
Justified in by the helicopters: As they were dropping off and picking up soldiers, they pretty much had to get down low. Indeed, the majority of the battle depicted in the movie was simply over control of the Landing Zone (the purpose of picking that particular LZ, of course, was to bait the NVA into a fight to confirm their location and test the effectiveness of the new Air Cavalry battle doctrine the Americans were using.)
Much of the air support was similarly justified, as at least some of it had to get low enough to identify the enemy and engage. In Real Life, one of the A-1 Skyraider attack planes crashed when it got caught by the fragmentation from one of its own bombs. Remember: the blast radius of any munitions dropped from an airplane includes the vertical dimension as well as the horizontal.
Rambo III. Rambo destroys the Big Bad in his Hind gunship by ramming it with the main gun of his tank. Yes, it was flying at the time. And making repeated low level swoops from the direction Rambo's weapons were pointing.
In Robin Hobb's Dragon Keeper, the titular dragons are misshapen and think themselves incapable of flight. The second book proves them wrong, as Heeby learns to fly. It is implied that Sintara and winged human Thymara can also learn.
Justified in Peter Pan. When Peter gets "wounded" by Hook, he believes himself unable to fly off of Marooner's Rock. The truth is that he's fine and can fly if he really wants to, but he takes his own imagination so seriously that there's nothing to do but leave him there.
In Cerberon by Fredric R. Stewart, the skraad, human-sized intelligent avians resembling bearded vultures fear flying in daylight because if they're spotted by humans, the humans will kill them.
Owls In The Family by Farley Mowat is a short book about the author's youth in Saskatoon, Saskatchewan and how he came to raise two baby owls at his home. The elder, named Wol (after how Owl spells his name in Winnie the Pooh), learned how to fly by accident after he wandered too far out onto a cottonwood branch and it broke. But Weeps, the younger, never learned. "I tried to teach him how by throwing him off the garage roof, but he wouldn't try. He would just shut his eyes, give a hopeless kind of moan, and fall like a rock without even opening his wings. Weeps didn't believe he could fly, and that was that."
In The House at Pooh Corner, one story has Pooh, Piglet, and Owl getting trapped in Owl's home, after a storm knocks the place sideways with the door where the ceiling once was. Pooh comes up with a plan for Piglet to be lifted on a rope to the door. Piglet tries to protest this by asking why Owl can't just fly out. Owl justifies it with a vague explanation about his wing muscles and not having enough room for take-off, but given his tendency to be a Know-Nothing Know-It-All, it's kind of suspect.
In the picture book Franklin in the Dark (also adapted as a story for the Animated Adaptation), Mr. Sparrow is afraid of heights, so sometimes, when nobody is looking, he puts on his parachute.
In A Clash of Kings, Stannis Baratheon explains his decision to abandon the Faith of Seven and convert to the worship of R'hllor by telling a story of an injured hunting hawk that he nursed back to health but that was afraid to fly too high and as a result always missed its strike.
Clark Kent on Smallville can't currently fly, but has demonstrated the ability when he was brainwashed (by his father). Every special guest Kryptonian we've seen has shown the ability (except for the deliberately-depowered Kandorians), and there is much needling. His cousin, Kara, says that he's holding himself back. He now has a Legionnaire ring, but the Legionnaires disabled its flight power so he'd have to learn it on his own. The creator's "no flights, no tights" rule is always getting pushed to more incredulous ends.
Averted (and possibly lampshaded) in Firefly. When Wash flies into a canyon to avoid chase... only for his pursuer to fly over the canyon. He then makes the best of the situation by ducking under a rock formation to give them some temporary cover while they figure out a solution.
30 Rock: Might be what Tracy Jordan was getting at in this clip, where he berates a pigeon eating his food "don't you know you can fly?"
Averted most of the time and justified the rest in Dungeons & Dragons, which addresses the problem of whether most flying creatures are capable of flying straight up. In the case of basically everything that isn't hovering, the answer is "no".
Zig-zagged in Warhammer 40,000. Some flying and hovering models, like jetbikes or creatures with wings, fight no differently in close combat than ground-based units (though they do get to ignore the effects of most terrain when moving). However, vehicles which can hover ("skimmers") have had rules making them harder to hit, depending on which edition of the game is being played and, as of 6th Edition, there are proper rules for flying vehicles and monstrous creatures, which allow them to fly well above the battlefield and avert the trope entirely.
The game has flying creatures, such as hippogryphs. However, prior to Cataclysm — at least in Kalimdor and the Eastern Kingdoms — the "flying" enemies acted like they had invisible feet. For example, you spot one on top of a short cliff and shoot it — and instead of flying straight at you, it took a very jerky path off to the side and down along the route you'd have had to walk if you were earthbound. There may still be a few mobs like this, but for the most part, the flying enemies actually fly now.
Outside a few specific quests (bombing runs and such), you can't engage in 3-dimensional combat even with a flying mount (as attacking causes you to dismount). However, killing somebody, getting on your flying mount, and hovering above the corpse out of enemy reach is a common method of ganking.
It's also possible, though tricky, to attack from above. One possible method is to dismount high above an opponent who's idle in the air, fire off a shot that stuns them, hopefully dropping them from the sky, and then activating a gadget to slow your fall.
Druids, who can enter flight form instantly (and thus can do this while falling) sometimes engage in aerial combat, but they don't really have enough spells they can use in the air to do it very much. Mages have more, but they can't remount — on the other hand, they have the Slow Fall spell.
Speaking of druids, one feral druid tactic called the "RAW Rbomb" involves shapeshifting out of flight form and into bear form in midair, drop down towards your target and casting Feral Charge when it's in range, which negates fall damage. In addition to allowing the druid to reach the target much more quickly (this is important when trying to hunt down rare monsters sought by many players), it also has the added coolness of a giant bear dropping down from the sky onto someone's unfortunate head.
An old druid game is "Aerial Chicken", which consists of flying really high, dismounting, and the one who re-mounts first (or splats into the ground) loses. Bonus points for convincing non-druids (who cannot re-mount while falling) to play.
Also played very straight in Dungeons & Dragons Online. All flying creatures simply hover, and dragons never fly in combat. Perhaps the most blatant example is the Velah raid. Velah is a red dragon who is seen flying throughout the raid, except when it comes time to fight her, when she lands and remains completely stationary, moving only her head and claws to attack those right in front of her (her back-side is protected by impassable rocks). Other dragons in the game do actually move around, but none use flight as part of their fighting strategy.
A similar situation during the final boss fight of Dragon Age: Origins is justified by having Riordan tear through the Archdemon's wing first, grounding it.
Averted in the MMORPG City of Heroes. A very common tactic when playing a character with the optional power of Flight is to shoot straight up in the air when a fight gets too ugly. The difficulty here lies in the fact that, being a Superhero/Supervillain game, there's a pretty darn good chance that your enemy can also fly, and in the case of AI-based enemies, much better than you can in a panic. The Sky Raiders, in particular, are a group of Rocketeer-esque villains whose entire shtick is jetpacks, and on the opposite side of things, Longbow has a habit of dispatching flying troops to cut the wings of flying villains. Also, there are so many ways to knock somebody out of the air or just plain ground them that virtually anybody with access to ranged attacks (and many people without them) can bring you down. As long as there's some ground around, jumpers are actually better at aerial combat than flyers.
Played annoyingly straight in the badly-written first Gameboy version of Winx. At several parts of the game, you are arbitrarily stopped by rocks on the path or falling down pits, even though the protagonists are, as the title suggests, more than capable of flight.
Somewhat subverted in Battle Stadium D.O.N. In the game, none of the Dragon Ball characters can fly, which makes sense, since the game would be kinda broken if they could, due to its gameplay. To make up for it, they can do quick dashes in the air.
Neverwinter Nights has the prestige class "red dragon disciple", wherein you draw strength from your draconic heritage and become more dragon-like, finally acquiring the half-dragon template. In the original RPG, this included the ability to fly, but due to the computer game's limited engine, flying just isn't an option. Which means that at higher levels, your character acquires a fancy pair of wings...that do nothing besides flap a little when you run.
Lampshaded by Deekin, a Dragon Disciple Bard in Hordes of the Underdark, who as well as being unable to fly with his own wings, sometimes wonders aloud why dragons spend so much time walking.
Also lampshaded by Kaelyn the Dove in Mask of the Betrayer, expansion pack to NWN 2, who claims that her wings are only ever useful as an occasional sunshade. For some reason, the benefit of wings from a mechanical point of view is a bonus to running speed.
The tabletop version of this class, along with the Half-Dragon racial template, has the wings be not quite perfectly formed on smaller creatures — they're not "draconic" enough. Flight is only possible for size Large creatures or larger with this template or class, contrary to physics. There are, however, feats that allow such creatures to fly; one such example is "Improved Dragon Wings" from Races of the Dragon.
Charizard and Dragonite, both of which have fully functional wings, could not learn the move Fly until the releases of Pokémon Yellow and Pokémon Gold and Silver, respectively. Oddly enough, Doduo and Dodrio, who seem to be based upon ostriches, have always been able to fly.
And also played straight with Bug Pokémon, many of which have fully functional wings, but only one, Volcarona, can learn Fly. There's a simple explanation: Fly isn't the HM that allows a Pokémon to fly. It's the one that allows them to carry a trainer while doing so. Flying-type Pokémon who can't learn Fly tend to lack strength, not capability.
Of course, this doesn't excuse cases like Spearow or Pidgey, both of whom can learn Fly, but neither of whom are larger than 1'00" tall nor weigh any more than 5 lbs. And let's not even get started the unique case of a Pikachu that learns Fly via an event...
An explanation offered by Bulbapedia is that the original Japanese name of the move could be read as "super jump," explaining how Doduo could learn the move (the Pokédex entry mentions it can jump very well). However, many future Pokémon were also noted as being able to jump well but couldn't learn the move.
The real explanation is right there in the game. In battle, Fly just involves jumping high and landing on the enemy, hence the low accuracy. Outside of battle, it involves transforming into a giant bird to carry the trainer.
This is muddled further by the addition of the move Bounce, an attack that's almost identical to Fly (to the point of being a Flying-type attack as well), but is clearly described as a super jump attack.
Beedrill, Venomoth, and Volcarona, despite being in perpetual flight, aren't considered Flying types due to them instead being Bug/Poison in the case of the former two and Bug/Fire in the case of the latter (Who's at least able to learn Fly, unlike the other two).
In the Pokémon Mystery Dungeon series, only some winged Pokemon move by flying, which grants them the useful ability to cross over water and pits. Other winged Pokemon like Pidgey and Salamence who choose to get around on foot are incapable of this.
Both Baten Kaitos games are offenders, particularly the first game where every playable character in the game has wings. The number of enemies that could easily be killed by hovering just out of their reach, the number of dungeons that could be easily completed by flying through them, and the general number of plot-relevant situations that could have been solved by the player characters actually using their ability to fly is staggering.
Colette from Tales of Symphonia gains a pair of fully functional wings after the first dungeon (Lloyd and Zelos also are shown to have them by the late game), but never seems to think to use them to fly across gorges to hit switches, get to out of the way treasure chests, or climb over an Insurmountable Waist High Fence, except for a few random cutscenes where she suddenly remembers she can fly.
Speaking of Tales games, Tales of Phantasia had a witch-like character who could use a flying broom. There are a couple situations where it's used to fly up (such as getting treasure chests too far to reach and avoid a dungeon that the other characters have to go through), though none that would desperately call for it.
Inverted by way of Plot Tailored to the Party in Tales of the World: Narikiri Dungeon 3. Several chests are blocked away on islands over bottomless pits or hot magma. The only way to get to them is by leading a party with Arche, the above Cute Witch, or Calo in the Witch or Arche costumes. (And no, you can't do it with Collette or her costume. Go figure.)
Winged Dreadlords in Warcraft III will sometimes ask, "If I have wings, why am I always walking?"
The Hind-D in the original Metal Gear. It remained on the ground, firing only its main gun. To add injury to insult, there's a spot on the map where Snake can stand and hit the Hind but it can't hit him.
Played straight with Donald Duck's bird form in the Pride Lands in Kingdom Hearts II.
MOBA game League of Legends, which is played at ground level, nevertheless has a champion that is a bird, two champions with wings (one of which flying), a levitating champion, and even one piloting a helicopter; with the appropriate skin, he turns into a Red Baron biplane or flying saucer. These can all be attacked with melee weapons from the ground. As a double whammy, the bird is the slowest champion in the game.
Averted somewhat in Grand Theft Auto: San Andreas. Once C.J. becomes pilot-trained, he can fly any plane wherever... except when the plot says 'No' or he tries to fly over the missile-equipped Area 69.
Played Straight, Averted, and Subverted in cutscenes of the Subspace Emissary ofSuper Smash Bros. Brawl:
Meta Knight actually seems to flip-flop in cutscenes. He flies low to the ground or runs when outside and traveling with others, but ascends to high height when he needs to save Lucas and Pokémon Trainer. He also flies through narrow indoor corridors, where you'd think running would be easier due to the size of his wingspan. Lastly, rather than flying up the entire way to the Halberd, he chooses instead to climb and leap up a mountain.
Flying animals in Zoo Tycoon 2, such as the secretary bird, may fly around, but it never occurs to them to cross their exhibit fences.
In Banjo-Kazooie, Kazooie can't fly until you specifically gain the ability from Bottles, and even then, it's only in specific places. In Tooie, she has to gain the ability to glide and doesn't get it until fairly late. She's a reasonably fast runner, though.
Fluzzard from Super Mario Galaxy 2, who is a giant parrot who, according to his hummingbird friends, is actually afraid of flying and prefers to glide instead, and is often used by Mario/Luigi to obtain Power Stars by having him fly to the finish line.
Flying units in Super Robot Wars can be intentionally moved along the ground by the players in case they need terrain bonuses, like, say, make a unit move into a forest to increase chances to evade. This is useful because most of the ground enemies can attack even if your units are in the air.
In Planescape: Torment, Fall-From-Grace is a succubus with leathery wings. Though rather squishy in melee combat and a gifted spellcaster, she never thinks to take flight either to escape a bad combat or to simply find a safe place to cast spells. Likewise, when pursuing the player, the gargoyle-like abishai never unfurl their wings and use their flight speed to keep up. They walk after a player who can run, enabling the player to evade them pretty easily. In 2nd Edition Dungeons & Dragons, which is the source of Torment's mechanics, both succubi and abishai could fly fairly quickly.
Similarly, Dragons in Baldur's Gate never take flight, even as things start to go south for them.
Dragons in The Elder Scrolls V: Skyrim do fly, but conveniently land within reach of a sword every once in a while, and never fly away from a battle unless the player shows no intention to fight. The Dragonrend shout serves almost exclusively to force a dragon to land so melee based characters can fight them.
In Sly Cooper, several of the enemies encountered by the player are birds. Some of them, like the dodos, cannot fly. However, there are others , such as vultures, herons or pigeons, that can do it, yet all of them prefer to fall to their deaths if knocked out from high places or into the water, instead of just coming back flying.
The Fire Emblem series has units with flying mounts like Pegasi or Wyverns, as well as some characters who flat out have wings of their own. While these characters do use their gift of flight to freely negotiate terrain, none of them seem to think of using it to attack from above and, instead, will hover just above ground level so the enemy can hit them. Particularly egregious if the ground-based enemy is the one initiating the attack and the unit is in no condition to fight.
In Unicorn Jelly, Lupiko is a witch who can fly on a broomstick — and is also afraid of heights.
"Get on the bird... Get on the bird... Get on the fucking bird!"
Similarly, The Nostalgia Critic pointed out the Fridge Logic in one episode of The Adventures of Sonic the Hedgehog, where Sonic and Tails were trapped in a cage, with the floor opening up beneath them. The Critic wonders why, if Tails could fly, he doesn't just pick up Sonic and get them out of danger.
Starshine, a superheroine from the Global Guardians PBEM Universe, often sniped at villains from a seemingly unassailable height (having both super-acute sight and a laser blast with no effective range limit). The one time she fought a villain who could match her for accuracy and range, however, she forgot she could gain altitude (going into orbit, if necessary... she could survive vacuum exposure, too), and instead dove and zig-zagged to avoid his fire.
In the movie Nukie, the title character tries to reach his brother in America despite the fact that he is stranded on Africa. Both of them are aliens who are capable of flying as the reviewer, The Cinema Snob, repeatedly points out, which would end the movie rather quickly. When Nukie finally suggests flying, the Snob's reaction is amazing to behold.
Cinema Snob: You don't. Fucking! SAY!!
In cartoons, this is often caused by replacing a generic animal in The Chase with a bird.
It's especially and extremely evident in any Tweety and Sylvester cartoon. Granted, the earliest incarnation of Tweety was colored pink because he was supposed to be a baby bird and thus unable to fly. His color change came about due to censorship, not any implications of him growing older.
Lampshaded in the cartoon Million Hare with Bugs Bunny and Daffy Duck racing each other to try to win $1M. Twice, Daffy is falling off a cliff (in one case towards a body of water) and Bugs remarks "I wonder if that silly duck will remember that he can [fly/swim]?" Of course, Daffy doesn't.
Daffy: Wow! I'm flying! I'm like a bird! Wait, I am a bird. I'm... like a plane!
Spoofed in an episode of Duck Dodgers where Daffy's clothes get mixed up with a Green Lantern's. He shoots up into the air, says he's the first of his kind to fly... all while a flock of ducks flies past in the background.
Another literal example is found in The Transformers (the TV series), The Transformers (the comic), and Transformers: War for Cybertron — Silverbolt, leader of the Aerialbots, is terrified of heights. In the cartoon, the Aerialbots were built on Cybertron out of the remains of old craft, with Silverbolt being built from a low-altitude shuttle, whose limitations were apparently carried over by Vector Sigma into Silverbolt's personality. Optimus Prime named him leader of the group to help keep his mind off of his weakness (though it may also be due to Silverbolt having the most level-headed personality among the Aerialbots, and being the only one of them to inherently respect other, weaker lifeforms such as humans).
Even worse off is the Autobot Triple Changer Broadside, whose alt-modes are jet fighter and aircraft carrier. Not only is he acrophobic, but he gets seasick on the water.
In addition, the majority of the Decepticons in the original series could fly. However, they still chose to run on foot most of the time, even in the title scene — in which the seekers transform out of their jet modes, land on the ground, and then rush the Autobots with guns blazing.
Transformers shows feature a number of instances when characters who are able to fly simply fall off a ledge anyway. Examples include the Decepticons falling into lava at the end of the episode Heavy Metal War, the Dinobots (among them Swoop, a flying robot-Pterosaur) falling into a tar pit in the two parter Dinobot Island, and various flight-capable Beast Wars characters doing the same, even when their flight gear is seemingly undamaged (Terrorsaur, in fact, dies this way).
In episode "Cootie Gras", the girls are trapped in a pit with a boy they think is afflicted with the terrible disease of "cooties". They run around in the pit, trying to dodge the cootie boy attempting to kiss them, never once attempting to fly and only doing so after they realize Cooties isn't really anything and let him have the kisses he was so eager for.
In another episode, Buttercup is being chased by the townspeople because she refused to take a bath. The chase scene was really intense, with Buttercup rushing through the woods, and suddenly, she stops and realises "Duh, I can fly." It seems really bad, since they actually float around at least half the time.
Lampshaded and played for laughs in Drawn Together. Captain Hero frequently stays in bad situations his superpowers could get him out of for various reasons. When the characters bring it up, it sometimes becomes a case of I Forgot I Could Fly. He points out that, while they were in a helicopter about to crash to death, that he could easily save them. Sadly, he can't as he is addicted to drugs. "Still think doing drugs is cool?"
Adventures of Sonic the Hedgehog: Any and all of the various flying (and occasionally climbing) Sonic characters have probably been subject to this at some point, in and out of the games. Granted, the thing that's after them may be very tall (and flying isn't as fast as running), but in some cases, it's just strange. For instance, there's a cutscene in Lava Reef Zone in Sonic 3 & Knuckles where Knuckles pushes a boulder down some stairs just after whichever character you're playing as (either Sonic or Tails) goes up them, knocking them back down again so they have to go up again. If playing as Tails, the game doesn't let you fly over the (slow-moving) boulder!
In Disney's Aladdin: The Series, there is at least one episode where Aladdin repeatedly tries to tell Genie to shape shift into a bird and carry them away, and Genie just doesn't get it. But then, Genie carried a chronic Idiot Ball in that entire series (much less so in the movies).
In the Donald Duck short Good Time for a Dime, Donald briefly tries to fly away from a rogue airplane ride, but it ends up not working at all, and he still plummets. By that time, his arms/wings were already anthropomorphic enough that they clearly weren't wings anymore, though.
In Teen Titans, Beast Boy seems to forget that he can change into a flying creature to get out of trouble (notably in the first episode with Mad Mod). Much of this is played for laughs or can be explained by remembering that Beast Boy isn't the brightest tool in the shed. Although, he DID outright state once or twice that his biggest issue was thinking which creature would actually be the most beneficial to a situation... Hence why him turning into a giant, heavy beast when on unstable footing was usually comedy relief. On occasion, he has tried to fly away and promptly been shot down by a ray-gun, force-field, or what-have-you. He also mentions at one point that transforming into a flying animal is very tiring.
Despite being explicitly shown to be capable of flying into the clouds, Appa from Avatar: The Last Airbender is frequently forced to dodge projectiles launched from catapults that couldn't be reaching heights of more than a couple hundred meters instead of just staying out of their range.
Superman tends to forget he can fly in Justice League, whenever he is fighting a ground-based foe like Solomon Grundy or Darkseid. The latter at least has the (almost) never-missing Omega Beams to make it so that keeping his distance via flight wouldn't really make Superman any safer. The most ridiculous example is in "War World", in which he is captured by Mongul and forced to fight Draaga, another alien, against his will. Despite making it very clear that he doesn't want to fight, Superman never thinks to just fly out of Draaga's reach and stay there.
The "forgot I could fly" variant of this trope occurs in the Regular Show episode "Death Punchies". Rigby abuses a forbidden kung-fu technique and ends up sending Mordecai and himself to a pit that's steadily filling with lava. After the two wail and moan and blame each other for their situation, Mordecai says he was smart enough to learn a way to escape, and uses another forbidden kung-fu technique to fly to safety. This is the only instance in which Mordecai has been able to fly, despite being a bird (specifically a blue jay, a species perfectly capable of flying).
Justified with Fluttershy in My Little Pony: Friendship Is Magic, who really is acrophobic — Spike even questions why a pegasus would be scared of heights. In her case, it's an extension of her fear of everything. Rainbow Dash, meanwhile, just seems to have an easier time maneuvering forward instead of up. Her nickname is "Rainbow Crash"... Fluttershy's phobia of heights was at its climax in "Dragonshy", wherein her wings would lock up at the mere sight of heights, leaving her unable to cross even small gaps that ponies without wings crossed with ease. Since then her fear of heights has been much tamer, and although she mostly sticks to the ground, she shows herself to be a physically weak, but competent flyer (in a pinch, even the weakness goes out the window as she can catch up with the aforementioned Rainbow Dash while trailing a not-air balloon behind her).
Justified in Cyberchase with Digit who literally has acrophobia or gets injured in a way that prevents him from flying.
One episode of American Dragon Jake Long, has Jake being kidnapped by the Huntsclan as part of a hunting ritual and chained to a bunch of other magical creatures with their own idiosyncrasies (including a mermaid with a phobia of water).
Many small forest birds avoid flying above the canopy as the treetop levels are much safer. The airspace above the treeline is where the larger predatory birds tend to hang out. However, all birds know enough to fly up out of reach of land-bound predators like cats.
Larger birds (such as condors and albatrosses) cannot fly straight up into the air and need a long running start (or elevated launch point) to get off the ground. The same goes for many species of waterfowl aside from dabbling ducks, particularly coots.
Long-winged birds like swifts are helpless when they end up on the ground — to fly away, they need to aim for the ground and miss. That they are obviously better at clinging to something than walking doesn't help.
Mother birds, most famously Lapwings and Killdeer, though other species have been observed to use this ruse as well, sometimes try to lure predators from their nests by feigning an injured wing. This necessarily keeps the mother down near the ground. However, once she's far enough away and feels the enemy has been sufficiently distracted, she'll fly up to startle the predator and break off the chase.
As some scientific studies and anyone who has chased pigeons will tell you, many ground-feeding birds won't fly unless they have to. Until they decide they can't reach that raised platform or can't escape that pursuer without flying, they'll try to do it on foot. Most birds will run up slopes while beating their wings for extra speed, rather than flying to the top, until the incline is almost completely vertical. This is because powered flying —particularly the takeoff part— is a rather energy-intensive activity, so the more a bird flies, the more food it needs to ingest afterwards.
In fact, some paleontologists theorize that this is how birds evolved flight in the first place, back when they were still dinosaurs. The theory is that feathers evolved as insulation, then got used by flapping to aid the dinosaurs in running up steep slopes. As feathers evolved to be better at this, they became possible to use for gliding. Then the dinos combined the two uses, and the rest is (pre)history.
Vampire bats are normally quite good at getting airborne, being among the few bats that can launch themselves from flat ground by jumping into the air. After a feeding, however, they are usually too heavy to take off and must hide in the underbrush until they've absorbed most of the blood's plasma into their own bloodstreams, at which point they pee like a waterfall to lighten themselves again.
Unfortunately, flying straight up does not work when attempting to escape from a car hurtling toward a bird at 50 mph. The car goes too fast and the bird can't get out of range fast enough. Ends with a splat on the windshield.
"Nap of the Earth" flying sometimes seems like this due to the likelihood of crashing, but can be safer than flying into the radar of enemy SAM defenses. It works by putting obstacles and the curvature of the Earth between you and the enemy radar. However, if your enemy mostly relies on guns or shoulder-launched or other small SAM systems (which are a lot more common than bigger, long-range ones) for air defense, it does make sense to fly higher to avoid them. Essentially, you have to decide if you are more concerned about the big missiles and guns that can reach you at high altitude (fly low, or use Wild Weasel tactics) or the smaller missiles and rapid fire anti-aircraft guns and small arms fire (fly high and fast).
This is the difference between British and American attack helicopter doctrines. The Americans use their helicopters to rain Death from Above, which is somewhat safer, whilst the British instead choose to prioritize lethality over safety.
When birds molt their flight feathers, they suffer an inevitable loss of wingpower, and some species do become temporarily flightless.
Hummingbirds are the only birds that cannot walk — so they have no choice.