Explosions in Space

A subtrope of Space Does Not Work That Way.

Hollywood is not interested in teaching or even researching physics, and generally doesn't even depict normal explosions on Earth accurately, so it's no surprise that explosions in space rely on Rule of Cool rather than science. In the movies, explosions in space work pretty much the same way explosions on Earth would (or rather the way film-makers imagine they would, with lots of red flames and smoke).

In reality, space has no air to transfer the explosive energy to. Thus, explosions would have an initial brilliant flash, and the resulting spherical fireball and debris would travel away from the point of explosion far too fast for the eye to see. The fireball would become transparent a few microseconds after the explosion due to cooling by radiation.

Nuclear explosions would be similar, but with a much brighter flash, and little or no visible debris since it would be vaporized.

Explosions in vacuum on the surface of a planet, moon, asteroid etc. will look similar to those in zero-g, but any debris that does not achieve escape velocity in the local gravity field will arc back down and rain to the surface. In low gravity, this could take minutes or even hours.

Further, if a spacecraft blows up, the explosion should have the same velocity as the craft did (possibly altered by the velocity of whatever hit it). I.e., the boom should keep moving. Many movies and shows have a fast-moving craft turn into a stationary explosion (relative to the camera).

Above all, explosions in vacuum would be silent.

In many cases, this is caused by the method of special effects: actual pyrotechnics in an atmosphere. It should be noted that this is generally considered an Acceptable Break From Reality by the majority of the audience.

Many Hollywood Explosions in Space will also include a Planar Shockwave.

This is such an ubiquitous trope that only aversions and subversions should be listed.

Exceptions

Anime and Manga

Most explosions in space combat scenes in most Gundam series' follow the more realistic quickly-fading spherical explosion pattern. There usually doesn't seem to be much debris, though, but it may just be vaporized by the Mobile Suit's compact reactors failing catastrophically.
Super Dimension Fortress Macross was also another big user of the spherical explosions, in or out of space.
Planetes, being on the hard end of the Mohs Scale of Science Fiction Hardness, spectacularly avert this. When a space center on the Moon where a giant spacecraft engine is constructed blows up, an immense cone of ejected matter is shown, in a realistic and terrifying way.

Film

In 2001: A Space Odyssey when Bowman blows the explosive bolt hatch, the sound of the explosion is cut short by the decompression.
In Silent Running, nuclear explosions in space are just circular flashes that fade away.
Shown accurately once (except for the sound) in The Fifth Element when Korben blows off the docking bay doors to escape the hotel, otherwise, used in every other explosion in the movie.
In Apollo 13, the explosion apparently quite accurately depicted the real life event.
Done correctly at the tail end of The Avengers. The nuke Iron Man steers into the enemy mothership detonates as an expanding sphere, with no Planar Shockwave or other Hollywood contrivance.

Literature

In the Honor Harrington series, ships that have their fusion bottle fail just have a "single, eye-searing flash," and then are gone.
- It's also mentioned that nuclear warheads are only useful as weapons in space if they get a direct hit (Which is highly unlikely), which is why missile weapons had moved on to using bomb-pumped lasers by the start of the series.
In Matthew Reilly's Area 7, when a space shuttle gets hit by a missile, it simply cracks.
In the American Robotech novels, explosions in space are always spherical.
In The City Who Fought, a starship whose drive systems are going critical explodes near the protagonists' space station, and the resulting debris field makes venturing outside extremely hazardous for quite a while.

Live Action TV

Like every Sci Fi show, Stargate has this. However, when they use nukes, the explosions are at least spherical and without a mushroom cloud.
In Firefly, damaged ships simply break up, the broken parts drifting in the trajectory of the ship.
In Battlestar Galactica, explosions usually die out quickly and fiery explosions (which are caused by oxygen in the ships that blow up themselves - the reason why Cylon raiders hardly ever blow up but just disintegrate mostly) appear 'smeared' by velocity. Also, nuclear explosions do appear mostly as 'just flashes' as described above, without the trope-ish fireball and/or mushroom clouds.
Babylon 5 generally managed this quite well.

Newspaper Comics

A The Far Side strip Lampshaded this trope: A scientist jumps up in a crowded theater, yelling "Stop the movie! Stop the movie! Explosions don't go 'boom' in a vacuum!"

Tabletop Games

Though the visual isn't discussed, explosions in GURPS lose about half of their power when in space due to lack of atmosphere.

Video Games

In EVE Online, the explosion effects look pretty much correct according to what is described above. They are slowed down, however, so that the players can savor in the shiny afterglow of the ship they just helped blow up.
- Nobody's perfect, though: Torpedoes still give a great planar shockwave. So do large structures when they go BOOM. Every time a Drone Silo is blown up, a planar shockwave comes with the explosion, free of charge.
- They do get the "Explosion moves on original trajectory at original velocity" bit, at least. Sadly, the same can't be said for the wreck that's left behind, though that's so you don't have to go chasing it down when you want to loot it.
Star Fox games do this as well, with ships mostly breaking apart after being hit or the classic "BOMB" item going in a perfect sphere.
Slyly justified in the early PC game Elite. The manual explained that when a ship or similar explodes in space, as well as the flash it produces a burst of radio waves which, hitting your communicator, make a sound just like an explosion.

Web Comics

A Miracle of Science is careful to make sure that the behaviour of explosions and smoke from stacks on the moon obeys real life physics. Though it does have smoke stacks on the moon...
Starslip lampshades this trope in a storyline about the Astry's combat exercises. One of the captains complains that the battle doesn't feel like the real thing—because the damage is all simulated, and there are no explosions in space when a ship is hit.

Capt. Zarde: Pyew! Pyow Bwommmkssrrch! Augh! This sucks!

The Inexplicable Adventures of Bob has shown space explosions twice so far. The first one was accompanied by the Unsound Effect "SILENT KABOOM!" The second one quickly morphed into a fireworks display, with the onlookers' screams changing to "Oooh! Ahhh!"

Real Life

Back in the day the two Superpowers conducted several series of high altitude nuclear explosions that resulted in fireballs being as cool if not cooler than anything Hollywood could produce well into the age of CGI. Just another example of something that's just as easy to get wrong as right. It should be noted that these explosions were still in the atmosphere, just very high up.
Nuclear explosions in space would cause damage in a very different way than nuclear explosions in an atmosphere. A nuclear explosion in a vacuum produces a bright flash, a burst of neutrons, and a burst of intense radiation that rapidly declines in effect due to the Inverse Square Law. The actual damage to a target would come from the radiation and neutrons, which would fry the crew plus any electronics, and leave the target highly radioactive.
A faulty spy satellite is said to have been shot down with a missile by the US Navy, to prevent it from becoming a hazard.