A very widespread trope in video games, especially in Side View, but can also be found in animations. All characters, no matter how slow they are otherwise, can turn their backs instantly. This is also due to difficulty constraints of implementing non-instant turning, making it one of the Acceptable Breaks from Reality.
In 2D games, it very often goes hand in hand with Ambidextrous Sprite. Even in several First Person Shooters (particularly on consoles), there may be a button which instantly turns the player by 180 degrees. It is also usually possible in 3D PC games to make a character spin dozens of revolutions per second with high mouse sensitivity, yet the character doesn't feel the effects of that. This trope dates to the second generation of video games, making it Older Than the NES.
When this trope is present in a multiplayer game, it is a good way to identify novices. If a player uses only keyboard controls they will turn at a slow fixed rate. Besides causing a severe maneuverability disadvantage, this is also obvious to other players and marks them as easy targets. It can also identify people using aimbots, as the code involved would cause the person using the aimbot to instantaneously lock on to the nearest enemy, even if it was behind the aimbotter.
Since this trope is ubiquitous, we list aversions instead of straight examples.
Partially in play in The Legend of Zelda: Spirit Tracks. Whenever you board your train from a town, you have to select a destination, which determines the direction your train is facing, even if there's no possible way your train could have turned around at most of the stations. An Acceptable Break from Reality, because without it you might have to take a detour or travel backwards (which is much slower) to the nearest intersection just to turn around, making the train trips very annoying.
The Tower Of Spirits, on the other hand, has an actual railroad turntable inside of it, so you always come out locomotive first.
The Atari 2600 version of Asteroids let the player activate a special power when pressing down on the joystick. By default, it's hyperspace (teleport randomly) but the player could replace that ability with a shield, instant 180 degree turns, or no special power at all.
Moon Crystal had a smoothly animated sprite which actually turned slowly. However, controls suffered a bit due to that.
Super Smash Bros. has relatively quick turning animations, but also allows the player to execute attacks mid-turn, so the animation is mostly cosmetic. Though there are weird tricks such as Shellshifting...
Played straight for Mr. Game & Watch for obvious reasons. Although it becomes averted when he's wielding a hammer in Melee as he can actually be seen slowly turning, likely due to a graphical oversight. This was fixed in subsequent games.
Sonic Battle averted this. Which Fight Pose Emerl has equipped is usually a cosmetic choice (though Gamma's causes him to explode on death), but it does affect how quickly he turns around. Chaos's, for example, is painfully slow.
Averted in the Deadliest Warrior videogame, to Spoony's chagrin. The game developers actually sent him a message about his complaints, saying that you don't make instant 180 degree turns in real life, and his response was "Yes you do! If someone is stabbing you in the back, I think you turn around pretty much instantaneously!"
In order to equalize online multiplayer between mouse, keyboard and flightstick players, the Descent series has a fixed maximum turning rate. Though it's most like an FPS, this may have something to do with the fact that it also resembles a flight sim to a certain extent.
Upcoming Interstellar Marines avert this and play it straight, at least in the playable demos that have been released so far. No matter your mouse sensitivity, if you try to do a 180 turn the game will slow you down. You can freely pull off instant turns in midair after jumping though.
Averted from the first series in Armored Core, reflecting the size and the apparent difficulty maneuvering the titular Humongous Mecha. The turning problem (if you can call it a "problem"; most players simply grow to live with it) are sometimes mitigated by boosters that explicitly allows for quick turns. In the 4 series, the trope is played straight, in that side boosters can be used to perform quick turns.
Players and NPCs can generally do this in World of Warcraft, so it is really obvious in the few situations where they can't. Several vehicles, such as vehicles on the Flame Leviathan encounter and mounts at the Argent Tournament, have a nonzero turning radius and time. It's generally the same as or close to the radius and time it would take for a player to turn if they used arrow keys, except that it can't be avoided by using the mouse.
It is also actually possible to make other players feel the effects of such rapid spinning to a degree: if another player sits in a passenger seat of a mount, rapid spinning will be shared by them, but they will not be expecting it.
Star Fox Adventures for Gamecube had the characters skid a moment and stop before turning around, sometimes causing a bit of frustration when avoiding enemies.
Averted in the Prince of Persia games after The Sands of Time: walking in one direction and then attempting to walk in the opposite direction without stopping would result in the character skidding to a halt before turning around.
In all Mario games, 2D or 3D, if you move in one direction and quickly slam the Control Stick in the opposite direction, Mario will skid a little; Luigi tends to skid more.
The above also applies to all Sonic the Hedgehog games to date. Although, in the 2D games at least, it's played straight if you're standing still, or moving very slowly, or if you are forced to by springs (sometimes the two close together facing each other).
In Sonic Unleashed, Sonic the Werehog not only does a full turning-around animation, but needs extra space for him to turn around in. This can result in some unintentional deaths if the player chooses to turn Sonic around when he's standing near a ledge he can't grab.
Strangely, in Super Mario World, Mario plays this straight, but certain enemies like Koopa Troopas and the Koopalings take a moment to turn around.
The Elder Scrolls II: Daggerfall mobile NPCs and monsters displayed their sprites from various angles. As programmed, this allowed them to turn around and turn corners. In practice, they always ran right at the PC against corners and walls and, depending on the speed of the computer, appeared to turn around instantaneously when approached from behind.
They do instant turns in Morrowind and Oblivion, too. Since everything is 3D, they should be able to at least rotate gradually, but often they don't.
The Paper Mario series lampshades this trope almost the entire game, where if you do an instant 180-degree turn (or an object does) it shows the object or person literally turning over as if you were flipping the piece of paper over instead of turning it around in a more real-life way. This looks especially funny when long trains and such perform this, as it takes forever for it to turn around in the first place.
The Wild ARMs games were notable for averting this; despite being sprites, turning in various directions will use animation.
Dragon Quest IX uses a touch screen to control the Celestial Express, so the train will gradually turn to follow the stylus. Even with a directional pad it will gradually turn to face the direction of the pad.
Somewhat unusually for an educational game that predates Legend of Zelda, Tonk in the Land of the Buddy-Bots featured fairly fluid turning animations that did take a beat to do. Considering the tight timing necessary in parts of the higher levels, it could make a difference.
Similar to Paper Mario, Elasto Mania and its prequel had the main character along with the body of the motorbike turn although the wheels remain intact although their front wheel and rear wheel roles are reversed.
When using the third-person Free Rotating Camera mode in Thief: Deadly Shadows, Garrett not only can't turn around quickly, but actually can't even turn around in-place (as one would in first-person view): he has to make a realistic (or "realistic") couple of steps in a small circle, which can mean death on a narrow ledge.
The main character of Resident Evil 4 walks slow, but can turn around quickly. Thank goodness for this feature, it is easy enough to get stuck in the middle of group of enemies.
The quick-spin was first seen in Resident Evil 3. Since the series uses tank-style controls, this was quickly seen as a blessing, and every game since has implemented it (including the Gamecube remake of the first).
When Leon (or Chris or Sheva) performs the 180 quick turn, he actually takes a step behind himself, with his foot turned almost all the way opposite from the direction he was originally facing. This is the fastest and most efficient way to turn around, showing that someone did the research, nice it's not generally a natural movement.
Annoyingly averted in Rule of Rose where Jennifer must actually walk a small circle to turn around; turning on the spot simply isn't possible in this game. Really annoying in the Mermaid Princess bossfight where you must avoid the titular monster's corrosive vomit, and more often than not end up walking straight into it when you direct Jennifer to run away.
An actual Ability of Soldiers/Tanks in Transformers: War for Cybertron, who can instantly switch to a backwards pointing position. This, combined with tanks having a powerful cannon, let tanks outmanuveur faster foes like Scouts/Cars. Needless to say, spinning 180 without a rearview mirror and snap-shotting an enemy is very much Difficult but Awesome.
In Jagged Alliance, characters take Time Units to turn. In Jagged Alliance 2, they may automatically turn as they raise their weapon as you enter view.
Averted by the X-COM series despite battles being turn-based. Soldiers have to use Time Units to turn in place and it is quite possible to spend an entire turn just twirling around or, more likely, come up a few TUs short of being able to take a shot because you had to turn to face the enemy. On the other hand, it is one of the very very few actions that do not trigger Reaction attacks from aliens looking at you.
The freeware game Sane features a version of this, with instant turns only possible if the character isn't moving, or moving very slowly. If the character has built up some speed, when the player tries to turn around, they have to skid to a stop first.