Streaming Stars

Real spaceships transiting the void move at incomprehensible speeds. However, you wouldn't know that by looking out the window. In media, this is unacceptable. A moving object must give the impression of speed and motion.

Enter the streaming star field. Look out the window or canopy of any TV or movie spaceship and you'll see a background of stars flowing past like telephone poles. This happens whether the spaceship is moving at sub- or super-luminal speeds (though super-luminal velocities will have some additional effects).

As Douglas Adams pointed out, space is big. This means that stars are really far away. Galaxies are even farther out. There will be very little Motion Parallax in a star field seen from a spaceship moving through the solar system or even between nearby stars. In captain dummy talk, that means you simply won't see a star move in relation to you, unless you're a) within said star's solar system (and then it'll just be the one), b) moving really, really fast, like cross-the-galaxy-in-a-day fast, or c) turning. Anyone who's driven down a long highway in a wide flat area can see this effect to a lesser extent: that mountain far to your left doesn't really seem to move much as you go. Our sun, and even just the Moon, which is much closer, give an even better example; they don't seem to move at all as you move.

In fact, even if you flew so fast that you could see star movement (but still sub-luminal), the actual view would surprise you: the stars before you would brighten and concentrate in the center of the field of view, while the ones behind you would dim and diverge all over the field of view.

Of course, from a production standpoint, even if you averted this trope, you could theoretically still convey motion just with the starship moving across the screen, though probably not in a way that says "warp speed"

Compare Space Flecks, a similar technique used to convey motion in video games.

Film

 * Variation and partial aversion in Star Wars. It uses the effect, but in fact it's only the reality warp of going into hyperspace. Once you're in hyperspace all you can see out the windows is a crazy blue energy tunnel that gives people migraines if they stare at it too long.
 * Both used and spoofed in Spaceballs. To catch up with a fleeing Lone Starr after he goes "light speed" (invoking Streaming Stars), the villains' spaceship shifts to "Ludicrous Speed"; this produces a plaid pattern. (That's pretty ludicrous all right...)
 * While not technically a streaming starfield, the Stargate sequence in  ~2001: A Space Odyssey~  deserves special mention.
 * Also the starfield in the exteriors moves because it just didn't look good if it didn't, Kubrick tried it the right way but went with wrong because it made for a better looking shot.
 * For that matter, the Stargate sequence from Stargate applies too.
 * However on a much smaller scale than most insulters - they are traveling at least ten lightyears in just a few seconds, so the speed is REALLY big. You can also always say that the wormhole actually travels through entirely different universe/dimension/portions of space etc., but that'd be just mean.
 * In both the film and the series, the stargate sequence is only there for the benefit of the audience and is mostly absent from later episodes (unless it's plot-relevant). The people traveling through the wormhole are dematerialized at this point and don't really exist as physical objects.
 * Alien. Originally the red-blue shift was to be used when the Nostromo was moving past light speed, but this was one case where dull realism was deemed more appropriate to the movie's dark tone.
 * The Soviet two-part film Moscow Cassiopeia shows blue streaming stars moving past the ship when viewed from the outside, despite the ship moving at near-light speeds (about 0.93c).

Live Action TV

 * Star Trek. When the series came back from the dead in the late 1970s, an attempt was made at a more accurate depiction of space, but everyone agreed it didn't look right for Star Trek, so they went back to the original style.
 * The episode "The Galileo Seven" even shows Streaming Stars rushing past the Enterprise when it's in orbit around a planet.
 * In Star Trek the Next Generation, the effect for stars at warp speed is upgraded to short, rainbow-colored streaks.
 * In Star Trek Deep Space Nine, a moving starfield view is justifiable, as the titular space station rotates... but the same windows change between panning and non-panning views in various episodes!
 * Battlestar Galactica Classic (old series only)
 * The Sid Sutton-designed title sequence used in Doctor Who, from 1980-1986.
 * Averted in Red Dwarf. The book even notes that Lister finds the view awe-inspiring at first, and later deeply boring.
 * Reverted in the 'Remastered' TV episodes, where the static view out of Lister's porthole was altered to make the stars move. Pretty much sums up the remastered episodes really...

Literature

 * In the Discworld universe, the stars are actually balls of fire about a mile wide, so this happens gradually as A'Tuin swims through space, and the constellations change regularly. It would actually be possible for a time traveler to identify the era by what stars are visible.
 * Averted in the Johnny Maxwell Trilogy, also by Terry Pratchett, where Wobbler creates a video game "Journey to Alpha Centauri". Apparently if you leave it running for several hundred years a message appears saying "Welcome to Alpha Centauri. Now go home," but the view doesn't change at any point along the way.
 * It changes. It just does it in real time.
 * Justified in The House On The Borderland, where the narrator sees stars wheeling overhead so fast that they appear as bright streaks circling the planet. As he's traveling forward in time at incredible speed, on his way to the end of the solar system, that's just how the Earth's own rotation would make the night skies look.
 * Averted in the Heechee Saga where the ships are described as catching up to light emitted from behind them and eventually just seeing a mottled sploch on the front viewscreen from all the old light.
 * In Alastair Reynolds House of Suns, Purslane's ship features a dining room that displays this image in its windows, purely because Purslane likes the effect.
 * Usually averted in Isaac Asimov's works - in Foundation it's stated that, in interstellar travel, the view only changes during hyperspace jumps. Even more notably, in Nemesis, seeing stars move during such one of these jumps is the first sign that something's wrong - it was a short test jump, stars weren't supposed to move perceptibly, but the ship had rotated while in hyperspace.

Video Games

 * Freelancer does that with tiny little particles that only show up when the viewpoint is moving. According to the manual, they're added by your ship's computer to make it easier for pilots to judge their speed at a glance. You can turn them off in the menu.
 * The Wing Commander series used tiny particles to show speed, too.
 * I-War with its Newtonian flight model does this with explicitly computer-generated reference points to help with maneuvers.
 * Elite II: Frontier and its sequel First Encounters, also both using a Newtonian flight model, have "stellar particles" which can be turned off, which is highly recommended for manual maneuvering.
 * Related: Basically many (if not all) 2D games that take place in space have the starfield background scroll, sometimes even with multiple layers of Motion Parallax. The problem with this is that if the camera isn't supposed to be rotating at all, just panning, then the parallax is so deep in space that it's imperceivable until utterly ludicrous speeds are reached. Darn if it doesn't look totally awesome, though.
 * Some 2D space games even combine the two, such as Ares, Galaga '88, and the Star Trek fangame Rescue!, which smoothly segue from scrolling stars at normal speeds to Streaming Stars at FTL speeds.
 * In this case, it's an Acceptable Break From Reality - the starry background is often the only way one can tell how one's ship is actually moving.
 * A truly bizarre incarnation of this trope appears in Diablo II: the starry background of the Arcane Sanctuary area is always moving while the character is standing still, the stars streaming towards the right. The stars move much more quickly towards the right when the character runs to the left, perhaps to strengthen the sense of movement in that direction. It sort of breaks down, however, when running in the opposite direction because the stars still accelerate towards the right.
 * "This was NOT designed by Nature's Architect" (The druid's line when he enters the Arcane Sanctuary)
 * Mass Effect shows this realistically; in the first game, whenever the Normandy moves from system to system, the loading screens show the light "approaching" (read: entering the mass effect envelope and moving faster) the Normandy as blue-shifted, while the light "trailing" (read: exiting the mass effect envelope) the Normandy as red-shifted. In the second game, while the Normandy is moving between systems, Shepard can walk around inside the ship and look out the windows in the observation decks or bridge, and the stars are shown barely moving at all, with blue-shifted light passing the vessel.
 * Neatly averted in Eve Online. When you initiate Warp, the only star will potentially move by is the one whose system you are currently in.
 * A regular background effect in Star Raiders, particularly when traveling through hyperspace.

Western Animation

 * This was played straight in both instances where The Backyardigans did a send-up of Star Trek.
 * A bizarre example takes place in Avatar: The Last Airbender when Aang is trying to "let the cosmic energy flow" through him as stars spin by. The starfield returns to normal as he lets go of transient attachments and accepts the reality of the Avatar Spirit... or at least that's what the Guru is trying to impress upon him.

Other

 * Microsoft Windows comes with a screensaver that shows this effect.
 * In the first BBC Radio Serial in the Journey Into Space trilogy, Operation Luna, they encounter UFOs during their return from the moon and black out; when they wake up and turn the cameras on to look outside, the stars are streaking past them. In a subversion, it turns out that this is because the ship is tumbling; even though the ship has been accelerated to time-bending speeds (accuracy only stretches so far, after all) once they get the tumble under control the observed motion is next to nil.
 * In a webcomic review for Sluggy Freelance of all places it's used as a backdrop for part of the video. Here's the link