"The Funeral of a Viking" (Frank B. Dicksee, 1893)
A subtrope of Burial at Sea in which the deceased (usually a warrior, but not necessarily a Viking) is laid in a boat with his effects, such as a sword, and set out to drift at sea. Then, a character (usually someone with emotional ties to the dead, or simply the most skilled archer present) lights a flaming arrow and shoots it at the sail. The ship is then engulfed in flame and slowly breaks up and sinks.
Played straight, it can be a Tear Jerker. When Played for Laughs, the character charged with shooting the flaming arrow will continually miss or fumble his bow.* When played historically accurately, a slave will be killed (and probably gotten known by her late master's companions) as part of the ceremony.
In some cases, the fire-arrow step isn't performed. This can be due to a lack of flammable sails and fire arrows, a need for haste, or simply different funerary practices.
A third variant exists in which the boat is not set out to sea, but instead used to lay the corpse in for a funeral pyre.
Note that some funerals may also add a living slave to the pyre as a Human Sacrifice.
And finally, Viking funerals need not be literal. Many examples feature metaphorical stand-ins for any of the aspects of the ritual.
Because this is a Death Trope, there are unmarked spoilers ahead. Read at your own risk.
Viking funerals are common amongst the Asgardians of the Marvel Universe. They have even been known to extend the practice to outsiders who prove themselves worthy. When Asgard was floating over Oklahoma (It Makes Sense in Context) they made funeral pyres with boats.
The eponymous V from V for Vendetta is given a funeral in the spirit of this trope, with the train acting as a proxy for the traditional boat. Instead of being shot with a fire arrow, the train is packed with explosives.
Lauren in DMZ is given one of these, although instead of a wooden boat and a flaming arrow it's an inflatable raft and a flare gun.
The beginning of the 1939 movie adaptation of Beau Geste shows the Geste brothers as boys giving a Viking funeral to a toy soldier by setting a toy boat on fire, and Michael expresses his wish to get a Viking funeral himself. Near the end of the movie, Digby fulfills Michael's wish by burning his body on an improvised pyre. Probably the first depiction of a Viking Funeral on film.
In S.O.B., the heroes decide their friend needs a better send-off than a Hollywood funeral full of phonies so they steal his body from the funeral home and send it out to sea in a burning boat.
In Van Helsing, the titular character gives the love interest this treatment after accidentally killing her.
The grandfather in Rocket Gibraltar.
The film Grand Theft Parsons revolves around the protagonist's attempt to keep his word to his friend, the late musician Gram Parsons, by burning his corpse in Joshua Tree National Park. Parsons' father wants a more conventional funeral, hence the need for the titular felony. Very loosely based on a true story; the movie adds a bitch-on-wheels ex as the main antagonist, presumably so the real (step)father who claimed the corpse (who probably has real lawyers) didn't have to be the heavy.
Played for laughs in the direct-to-video film Eulogy.
V gets one in V for Vendetta, his body is laid to rest in the train that delivers his bomb to the British Parliament.
Unsurprisingly considering it's a tale of an Arab experiencing Viking culture, two of these feature in the film version of The 13th Warrior, one near the beginning and one near the end of the film.
In What's New Pussycat?, psychiatrist Peter Sellers, suffering a case of unrequited lust, attempts suicide by Viking funeral, wrapping himself in a Norwegian flag and intending to set himself ablaze with a road flare in a rowboat on a Paris riverfront. He's rudely interrupted by Woody Allen, who chooses the spot for a sit down dinner.
In Troy, this is standard practice for both Greek and Trojan heroes.
One of the last scenes of Peter Jackson's The Fellowship of the Ring shows Boromir's body laid out in a boat and drifting over the waterfall of the Anduin.
In Thor: The Dark World, Frigga and the others who fell during the dark elves' invasion of Asgard are given a mass funeral, each set out on their own boat and set on fire by arrows.
Beasts Of The Southern Wild: Hushpuppy gives this kind of funeral for his father, Wink, with her friends and their families, mostly survivors of the storm, watching in respect.
The probable Trope Maker is the funeral of King Scyld of Denmark in Beowulf. Scyld's funeral boat is not set on fire, though. Note that Beowulf himself is buried more conventionally, by cremation on a pyre and the remains being put into a mound.
Prose Edda: The pyre of the god Baldur is built on a ship which is pushed out to sea as the pyre is kindled. Trope Codifier.
A very fine how-to-guide appears in the 13th century Heimskringla in the description of the funeral of King Haki of Sweden. This variant involves fire.
Discussed early on in the P. C. Wren's adventure novel Beau Geste (1924), when the three Geste brothers stage a "Viking's funeral" with a lead soldier and a toy boat set on fire, and the twelve-year-old Michael "Beau" Geste expresses his wish to be buried in this way. Many years later, his brother Digby fulfills his wish by burning Michael's body on an improvised pyre (thought without a boat).
The Lord of the Rings: At the beginning of The Two Towers, Boromir is laid to rest by Aragorn, Gimli and Legolas in one of the Fellowship's elven boats with his weapons and the swords of the orcs he killed when defending Merry and Pippin. The boat is then pushed into the Anduin and allowed to tumble over the waterfall. This treatment is justified in-story by the fact there is not enough time to give him a "proper" burial, but given that J. R. R. Tolkien studied Beowulf extensively, it is likely he was influenced by the funeral of King Scyld.
The Silver Horde in Interesting Times plan to give Teach such a funeral. In fact they plan to give him every barbarian funeral they can think of.
Cohen:In a longship set on fire, on top of a heap of the bodies of his enemies, under a burial mound.
In the Doctor Who Expanded Universe short story collection Short Trips: Time Signature, several of the stories involve the Sixth Doctor trying to show his companion, William, some Vikings. He never succeeds, but after William's death, the Eighth Doctor takes his ashes to Vinland, and arranges for him to have a Viking funeral.
In the finale of the Conan the Barbarian story, "Queen of the Black Coast," Conan sees off one of his greatest loves, the pirate queen Belit, like this, turning her ship into a funeral pyre and sending it out to sea.
In A Song of Ice and Fire, this is the customary burial rite for the riverlands lords. Played for some laughs at Hoster Tully's funeral, when Edmure repeatedly fails to hit his father's boat with a flaming arrow.
Khal Drogo gets the third variant plus slave, only the slave is the woman who killed him.
Victarion Greyjoy peforms a rather horrific variation when he sacrifices some maidens to the Drowned God and R'ollor the lord of light by giving them a Viking funeral while they're still alive.
In The Dark Is Rising: Will gets the sixth and last sign from a great ship, carrying a long dead king who was a an ally of the Light (but not King Arthur), and all his possessions. After he claims it, in an act of spite the Dark sets the whole ship on fire. Will is horrified by it, but Merry points out that Dark was so eager to be spiteful that they didn't think it through. All they have done is give the King a Viking Funeral, which is exactly what he deserves.
Vikings probably had the single most straight and well researched version of this trope ever shown on television; having been taken directly from Ahmed Ibn Fadlan's account of the Russ. It comes complete with fighting, drinking and other festivitites and a slave girl being sacrificed and having sex with a couple of men who say "tell your master I did this out of my love for him", which is taken directly from Ibn Fadlan's account. It even has an 'angel of death' overseeing the sacrifice. They sidestep the possible problems of shooting an arrow by just lighting the pyre on the longship while it's at anchor.
In the Doctor Who episode "The Impossible Astronaut", the Doctor gets one of these. "Last of the Time Lords" featured The Master getting one as well. The in-universe reason is that a Time Lord's body, to any other species, is considered a miracle of nature, and sufficiently-advanced societies could potentially reverse-engineer some kind of bio-WMD from even a single cell.
In the Fringe episode "The Day We Died", Peter Bishop performs one for his wife, Olivia Dunham.
In Merlin, Merlin gives one to Freya, sending her floating on a lake before setting her body on fire magically, from afar.
Happens again in Lancelot's second funeral. It's the same lake. Since he Came Back Wrong the first time, this is partially as a gesture of respect and partially a way to insure it never happens again.
In the Grand Finale, Merlin sends off Arthur also in this manner, except that he does not set fire to the body. Earlier in Series 5, the Camelot court give this to Elyan
Mysterious Ways: Performed for a character in "Something Fishy," although they light the boat on fire with torches before setting it out to drift rather than doing the flaming arrow thing.
Peggy: It's a Viking funeral. Miranda: Yep. Peggy: Isn't this illegal? Miranda: Yep.
Spoofed in one episode of Malcolm in the Middle, when Francis discovers a dead janitor in a hidden closet at Marlin Academy. He decides, along with several other cadets, to give the corpse a send-off worthy of a Viking prince by loading it into a dinghy, along with the janitor's worldly goods, dousing the whole thing with half a can of gasoline, lighting it and giving it a good push into the lake. Unfortunately one of the other cadets has left the rest of the can of gasoline in the dinghy, and the whole thing drifts into Commandant Spangler's boathouse just as the can ignites, thereby causing it to explode.
During Season 1 of The Tribe, Zoot, the psychotic leader of tribe Locos, gets a Viking-style sendoff as well. This is mainly because the local cemetary has been overrun by members of a hostile rival tribe, but also because (as his brother Bray explains) " Zoot thought of himself as a warrior chief."
Played for laughs in one of Rose's stories on The Golden Girls. She says one of her relatives was being given a Viking funeral, but the fire department kept putting it out.
At the end of "A Reunion ...", the second-season premiere of Don't Trust the B---- in Apartment 23, James van der Beek, having abandoned the idea of a Dawson's CreekReunion Show, decides to put the past behind him by loading a DVD boxed set of the series and other memorabilia on a rowboat in the Central Park lake and lighting it on fire.
Supernatural: Hunters usually give their fallen comrades the third variation to prevent their ghosts from rising.
The Manowar ballad "Swords In The Wind" references the funeral-pyre version of this trope, owing to the band's general love of Vikings and warriors in general.
Place my body on a ship, and burn it in the sea
Let my spirit rise, Valkyries carry me
Take me to Valhalla, where my brothers wait for me
While Dianna read The Rime of the Ancient Mariner, for some reason. It does have very roughly the right portentous, marine feel, and the person in question had spent centuries trying to die, so points for the vague Flying Dutchman tie-in, but viewers who recognized the poem were still somewhat taken aback. What kind of elegy is that for a Viking prince?
In Kick Buttowski Gunther gives Kick's helmet a viking funeral. We even see nordic god/ancestor constellation entities watching the funeral.
Dragon Age: Origins: It appears to be tradition in Ferelden. After the siege, the dead of Redcliffe are sent off in floating pyres. In the Return to Ostagar DLC, this is the most respectful send-off you can give the late King.
The vikings themself (duh) as reported by Ahmad ibn Fadlan. Also, archaeologists have discovered viking age and pre-viking iron age graves in Scandinavia where the ship was burned on dry land.
Apparently, certain pet owners found it a more interesting alternative to burial in the garden. You can try searching for "viking funeral" on Youtube; chances are there won't be many film scenes among search results.
Ensign Jesse L. Brown, the first African-American naval aviator could qualify. His plane was shot down during the battle of the Chosin Reservoir. His aircraft crashed, and despite rescue attempts he died trapped in the wreckage. To prevent his body or the plane from falling into enemy hands, a flight of naval aircraft dropped Napalm on the wreckage, as a pilot recited the Lord's Prayer.