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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Anime and Manga
Mobile Suit Gundam: which actually explodes 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.
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 Jack Campbell's The Lost Fleet 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.
Live Action TV
Red Dwarf, although these were far smaller and contained ashes.
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.
Done a couple of times on Babylon 5, most memorably 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. 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.
Worth noting, Commander Ivanova appeared to have memorized the list of names to be read at the memorial, rather than reading from notes.
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.
Star Trek: Voyager ("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.
This practice carries over into various Star Trek novels as well. When a civilian ship, shuttle, or other vessel without torpedoes suffers a casualty, it seems to be standard practice to use the transporter to do the job (optionally destroying the body in the process so there aren't desiccated corpses floating in deep space for all eternity...).
Wing Commander has one of these whenever one of the pilots (including the player) dies.
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.
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, but fortunately, the crew survived.