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.
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.
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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.
In the DCAU tie-in Justice League comic story "Disarmed", Green Lantern evicts an alien bomb off of Earth, making a comment that he never gets used to how quiet explosions are in space. The explosion is represented primarily as a sphere of light (with pointy bits on the compass points).
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.
Most of Star Wars plays this trope quite straight, but in the climactic assault on the first Death Star, one unfortunate Y-Wing is shown continuing to move as it is destroyed.
Also done correctly with the orbital cascade effect in Gravity.
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'sArea 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.
The History of the Galaxy series generally tends to describe explosions in space correctly. Usually, the danger is not the explosion itself, but the debris flying from the exploding ship or station in every direction at high speeds.
In another novel, a hyper-advanced ship (officially classified as a light cruiser but with enough firepower to take out a conventional fleet) is mentioned to be armed to the teeth with nuclear missiles. The author then proceeds to explain that, in space, this really isn't as dangerous as it sounds. With advanced point-defense systems and EM shielding (protecting from nuclear radiation and EMP), a ship can be effectively immune to a nuclear barrage, as nuclear explosions (without any matter to "feed" on or air to move) only have an effective range of a few miles.
In The Lost Fleet, ships explode in a brief bright flash only in two cases: reactor containment fails, or two ships collide at an appreciable fraction of the speed of light (ships normally maneuver at 10% of c). In both cases, little is left of the ship after the flash. Most ships that are destroyed in battle simply break apart and continue on their original trajectory, as pieces start to move apart.
In Robert A. Heinlein's Between Planets it is done correctly when Circum-Terra Station was destroyed by a nuclear weapon. The blast was described as a second sun, blazing white, and as an expanding, perfectly geometrical sphere. The story also explicitly states that there would not be a mushroom cloud in the vacuum of space.
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.
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!"
Though the visual isn't discussed, explosions in GURPS lose about half of their power when in space due to lack of atmosphere.
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.
While Dead Space games gets the workings of gravity and vacuum right most of the time, in the second game there is a curious exception. In a zero-gravity area (with oxygen) there is a large, roaring fire. Despite the lack of gravity, the flames are reaching "upwards", instead of expanding in all directions.
In Sword of the Stars nukes produce a small spherical blast in space, and the only other explosives are acid and nanite bombs that leave a sphere-shaped corrosive cloud. And when used in Orbital Bombardment nukes produce a sphere again but substantially bigger.
When ships are destroyed, their parts continue to travel in the same direction for a few seconds before they blow up. This is even true of Liir ships which, technically, don't move in the Newtonian sense but teleport millions of times per second. Thus, when Liir ships are destroyed, their wrecks should stay relatively at rest.
A Miracle of Science is careful to make sure to accurately portray the behaviour of explosions in space and waste gases from factory smokestacks on the Moon (It Makes Sense in Context, amazingly) that can be seen in the background of one page. Suffice it to say that the comic's creators really like to Show Their Work.
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. Note that most satellites are actually still within the atmosphere. (GPS satellites and the geosynchronous communication satellites used by everyday fixed dish antennas are two notable exceptions.)