Because Space Is an Ocean, you need some equivalent of Burial at Sea. And because you can't really throw a dead body over the "side" of a space ship, some more dramatic means of getting the body out of the ship is required.
Usually the deceased in placed in a "space coffin". In some cases the coffin is actually a torpedo, which is shot out of the ship's torpedo tubes. It may even explode, indicating that not only is it a torpedo but that it is actually armed. In less drastic examples, the coffin is taken out through the airlocks by mourners in space suits and allowed to simply drift off into space. Alternatively, you could Hurl It into the Sun - cremation by star is not that bad of a funeral.
As a Death Trope, all Spoilers will be unmarked ahead. Beware.
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Mobile Suit Gundam gives us the burial of Captain Paolo Cassius... with the capsule actually exploding after moving a safe distance away from the ship.
Uchuu Senkan Yamato: there are at least two space funerals held after major battles, both to some degree censored in Star Blazers. Long lines of space coffins are set to drift in space, presumably forever.
The funeral in the third season is actually said to be a funeral for dead enemies, rather than crewmembers. Whether this is a case of Bowdlerization or Woolseyism is an open question, since on the one hand giving your enemies an honorable burial is a, well, really honorable thing to do. On the other hand.. they obviously just didn't want to have to talk about named characters dying that early in the season. Also, you can briefly see the characters through the windows in their coffins so I don't see how they were planning to fool anybody..
In Planetes, astronauts at one point occasionally chose to be buried in a space coffin, but the practise has been banned by the time the show is set. One episode deals with the consequences of debris section finding such a coffin.
The Captain Harlock movie Arcadia of My Youth ends with this type of ceremony.
Crest of the Stars has a planet that sends their dead into space on a rocket, the protagonists manage to escape said planet by hiding in a coffin.
The Black Hole has the "humanoid robots" perform one of these for one of their own, which is another clue towards The Reveal.
Kane's body in Alien is jettisoned into space after the Alien bursts out of his chest. Traumatised after his unexpected death, the crew can find no last words to say about their shipmate.
In 2001: A Space Odyssey, Dave Bowman releases Frank Poole's body into space mainly because he needs both of the space pod's arms to open the emergency airlock. (In the novel, after deactivating HAL he does the same with the men killed in hibernation. In the 3001 novel, Frank gets better.)
Conquest of Space (1955). Because his decomposing body would poison the air, a deceased crewman is secured outside the spaceship. Realising the sight of his body drifting outside the viewport is affecting morale, the captain pushes the body off into space after a moving eulogy.
Enemy Mine has this in one scene, but with a twist of War Is Hell impersonality: the casualties from the Drac War are so numerous, that the coffins are constantly being loaded into the airlock by an automatic conveyor belt, stopping just long enough for the bored technicians on duty to check the deceased's religion and play the appropriate prerecorded last rites.
Not shown, but is a plot point in Outland. Marshal O'Niel wants to know where the bodies of the miners who've died after going crazy have gone. He's told they're taken away on the shuttle and Thrown Out the Airlock halfway to the space station. "Burial at sea, and all that." Of course, this is a useful way of ensuring there are no bodies around to autopsy.
The Ur Example was dreamed up by (who else?) Jules Verne, whose heroes bury a canine astronaut in Around The Moon.
The Mote in God's Eye. The bodies of the Marines who died evacuating the battlecruiser MacArthur were shot out into space from Lenin's torpedo tubes. They were then vaporized by blasts from Lenin's weapons, so the Moties couldn't retrieve the bodies and study them.
In Starman Jones, after Dr. Hendrix dies his body is set adrift in space, to wander the stars forever.
In Heinlein's later novel Time Enough for Love, Lazarus Long discusses how he did this to Andy Libby after the unfortunate fellow was mauled by a bear. Later, in The Number of the Beast, he uses Time Travel to go back and retrieve Andy's corpse so it can be rejuvenated.
In Alastair Reynolds' Revelation Space universe, one standard way to inter bodies is to accelerate in a spaceship until you're traveling as close to the speed of light as you get, then shoot the body out in front of the ship. This is referred to as "burial at c".
In C. J. Cherryh's The Faded Sun, this is the preferred burial of warrior-caste mri. In the whole Allience Union universe, being sent to the sun seems to be the preferred burial method among those identify themselves as spacers.
In Asimov's short story "C-Chute", the eponymous item is a euphemism for "casualty chute", which itself is a euphemism for / abbreviation of "chute used to eject coffins into space". The protagonist uses one to exit from the ship, because the part in which he and the other humans are imprisoned doesn't include any of the airlocks. To avoid alerting the aliens who have captured the ship, and thereby recapture it, he re-enters by an equally unconventional route.
Corran's father's ashes were left to drift in space, apparently not in a container. While dating the daughter of his father's mortal enemy, he once jokes that his father's ashes are trying to coalesce to stop him.
The drifting coffins variety seems to be the most popular version of this trope when a pilot's body can be recovered, appearing in several Meaningful Funerals. They're often tractored out into space and nudged towards the star.
When a body can't be recovered, as happened to Jesmin Ackbar, a torpedo is used as a symbolic stand-in.
Allegiance has a mortally wounded spacer named Tannis ask Mara Jade that she "bury him in space". She does.
In a variation, Alderaanians mostly have their space coffins shot into "the Graveyard", the shattered remnants of their destroyed planet.
In Halo: The Fall of Reach the bodies of the Spartans that "washed out" (read: died) of the augmentation process are launched out of the torpedo tubes of a ship with appropriate military funeral procession.
In the Honorverse, Grayson Armsmen are traditionally buried where they fall. When one of her armsmen dies aboard ship (in At All Costs), they eject him into space.
The traditional Jorenian funeral in S. L. Viehl's Stardoc series consists of this. The Jorenians normally attempt to put their dead on a course that would result in cremation by star or by atmospheric reentry, but it doesn't always work out as planned (as the events of Plague of Memory can attest).
In John Hemry's Paul Sinclair novel A Just Determination, a crewman is buried in space. His final trajectory is set for the sun.
In the novel Invincible, the fleet no longer has capacity to bring back its dead. Geary arranges for the corpses to be launched into the sun — and those of their enemies as well, since they do not know their funeral customs.
It's a fleet regulation that traitors not be buried in normal space. Instead, they are required to be buried in jumpspace. When Geary finds out, he is horrified at the prospect of someone (even a traitor) never being able to join his or her ancestors and the living stars. He calms down when Desjani points out that the act is purely symbolic in nature. Of course the ancestors and the living stars would be able to find anyone even in jumpspace.
The 'coffins' were far smaller and contained ashes.
When the "prime" Rimmer takes up the torch of the dimension-hopping space hero "Ace Rimmer" he and Lister place the previous Ace's holo-bee in a small capsule and shoot it into a planetary ring composed of similar holo-bee coffins.
In V, one of the female villains ends up sharing a space coffin with the man she arranged to have killed. Only she isn't yet dead when they launch it into space.
Most memorably done in the episode "Ceremonies of Light and Dark", wherein those crew who died in the previous episode's battle were given a mass funeral, with a whole line of space coffins being shot at the star Epsilon Eridani, escorted part of the way by a formation of Starfury space fighters. Worth noting, Commander Ivanova appeared to have used her Photographic Memory to memorize the list of names to be read at the memorial, rather than reading from notes.
A few episodes later, when Kosh dies, his encounter suit is placed in his Vorlon transport, and it flies itself into the star for an alien version of this trope.
In the reimagined Battlestar Galactica, there are several funerals after which the bodies are ejected into space from a Viper launch tube.
The ashes of the "fake" Hera were scattered into space from the open door of a Raptor.
It can be said that the whole Fleet receives one in the final episode along with Sam by way of being flown into Sol.
The original Battlestar Galactica also did it a number of times. One notable occasion occurred in the episode "Take the Celestra", where an elderly captain had made a Heroic Sacrifice during the attempt to retake the titular factory ship from mutineers.
"Latent Image": A photon torpedo casing is fired into a sun, bearing the body of dead ensign Jetal.
Also in "One Small Step" where the crew has a funeral with full honors for an early space explorer.
Wing Commander: Almost any pilot (including the player) that dies gets one of these, complete with 21 gun salute as the funeral crew sends the coffin flying into space. In the first game, if it's a wingman that dies Blair vows to avenge the dead pilot... even if he is the reason they died, in an Unfriendly Fire situation.
Happens in one of the cinematics of StarCraft. It's implied to be Vice-Admiral Stukov's, since it's his death they're lying about in the voice-over.
This trope is mentioned in the Chzo Mythos, where one of the astronauts mentions that it was popular in the 21st century for people to send their remains into space. Too bad the Space Coffin they stumble across contains the remains of John Defoe.
Justice League Unlimited. After Wonder Woman stops the Legion of Doom from stealing the Viking Prince's body, she gives him a Viking funeral... IN SPACE! This has the very practical goal of either having the sun's fusion destroy the body, or at least keep the Legion from another attempt.
Parodied in the Family Guy episode where Stewie's teddy bear is accidentally shipped away, and as a result he and Brian try to get it back.
A portion of Gene Roddenberry's ashes were put in a capsule and launched into low earth orbit, where it stayed for a few months before re-entering the atmosphere.
James Doohan's ashes were also launched into space, but returned to Earth much sooner.
A portion of Gene Shoemaker's ashes were placed on the Lunar Prospector probe that was deliberately crashed into the Moon in 1999, making Shoemaker the only human to be buried on another world.
Clyde Tombaugh has gone one better. Some of the ashes of the discoverer of Pluto are aboard the New Horizons spacecraft, due to fly past Pluto in 2015 before leaving the solar system. Cue the jokes about the IAU delisting Pluto so he could power New Horizons by spinning in his grave.
Apollo 13, almost. Plans for a burial-at-space, similar to a burial-at-sea, were made to be performed in case of a disaster (specifically, if the Landing Vehicle failed to lift off from the Lunar surface), but fortunately, the crew survived. If the unthinkable did happen, they would probably have read out the eulogy written for Apollo 11.
Fate has ordained that the men who went to the moon to explore in peace will stay on the moon to rest in peace.
These brave men, Neil Armstrong and Edwin Aldrin, know that there is no hope for their recovery. But they also know that there is hope for mankind in their sacrifice.
These two men are laying down their lives in mankind's most noble goal: the search for truth and understanding.
They will be mourned by their families and friends; they will be mourned by their nation; they will be mourned by the people of the world; they will be mourned by a Mother Earth that dared send two of her sons into the unknown.
In their exploration, they stirred the people of the world to feel as one; in their sacrifice, they bind more tightly the brotherhood of man.
In ancient days, men looked at stars and saw their heroes in the constellations. In modern times, we do much the same, but our heroes are epic men of flesh and blood.
Others will follow and surely find their way home. Man's search will not be denied. But these men were the first, and they will remain the foremost in our hearts.
For every human being who looks up at the moon in the nights to come will know that there is some corner of another world that is forever mankind.
—William Safire, speech drafted for President Nixon "in the event of a Moon Disaster". Before the speech, the president was to telephone each widow-to-be, and after the speech, communication to the Apollo Vehicle was to be shut off and a clergyman was to conduct the Burial-at-Sea liturgy.
During the Gemini program, the question was raised as to what action to take if an astronaut died during an EVA, since it would be impossible for his colleague to fit the body back into the cramped cabin. The initial instruction was to re-enter with the hatch open, towing the body behind the capsule on its safety tether. Only after it was pointed out that this would result in the capsule burning up was the decision changed to "Okay, cut him loose."