The 1800s.

In the 1800s, as academic history was still a young discipline, a set of ideas known as cultural history dominated most historical and antiquarian work. Basically, the underlying assumption was that everybody had a culture, and if you knew what culture a person belonged to, you could tell a lot about that person. So people that studied the past spent a lot of time putting things into boxes. Is this axe Frankish or Slavic? Is this brooch Roman or Germanic? Is this myth Celtic or Anglo-Saxon? Is this cemetery Christian or Viking?

Prior to the 1800s, the word 'viking' in Old Norse and Old English was used only to describe a job: being a pirate. But during the 1800s, people started to classify all the things that they thought went with being a viking—carrying swords, believing in Valhalla, having blond hair and blue eyes—and they lumped all these things under the capital-V 'Viking' term which we use today.

Nevermind that the cultural characteristics grouped under the term Viking were poorly attested, difficult to prove, and likely varied tremendously over time and space, between 793 and 1066, and between Newfoundland and Baghdad. And nevermind that only a very small percentage of the people that we call 'Vikings' actually did 'viking' things. Using the word Viking to describe a culture in this way has helped scholars group things together, and the 1800s it helped them talk about the early Middle Ages in a way that made sense to people living through the rise of nation-states.

It's also proven to be a powerful and enduring heuristic device. Even though we know that the term is loaded and misrepresents as much as it represents, we continue to use it today. (I personally prefer the term Norse, which still has many of the same problems.)

But what about reality?

That's messy. Few of the people who did become vikings—i.e. pirates—used swords. Swords were prestigious items, preserved for the elite, and at least in some places (Gotland comes to mind) the elite seem to have preferred using a seax. A seax is a one-edged long knife, sort of like a machete. Most regular vikings, however, probably used spears.

Whatever the weapon, did these people need to die with it in their hand? There's no solid reason to think so. People in Viking-Age Scandinavia didn't write much down. There's picture stones, which contain some images that we can identify with mythic figures like Sigurd and Thor. And later on you get rune stones, but many of these were actually Christian monuments and talk about praying for the soul of the deceased.

Most of our knowledge of Viking-Age mythology comes from stories that were recorded much later by a Christian chieftain living among the poor farming communities of Iceland. He had some interesting stories about Valhalla, but it's hard to know just how well these represent the stories that had circulated 200 or 400 years earlier. And if they were authentic, it's even harder to know how widespread these stories were. Perhaps they had been invented in Iceland to make the pagan myths seem more coherent and to answer questions being brought up by Christian missionaries (like, Where do you go when you die?). Christian Iceland was a poor and violent place, and you'd have to try pretty hard to make pagan Iceland seem any more brutal.

So the vast majority of people living during the Viking Age didn't die with swords in their hands. Very few of them likely died with weapons of any kind in their hands. And probably nobody saw a problem with this. So how were they buried?

Pretty much every way imaginable. In most cemeteries, there's obvious imbalances. Either most people are male, or female, or rich, or something else. These imbalances suggest that at least in some communities, not everybody got buried. Historical texts don't tell us what would have happened to them, and archaeology hasn't turned up further clues. Perhaps their corpses were left abandoned in the woods. Or perhaps they were dumped into the sea.

For those who did get buried, it's a mix between inhumation and cremation. In the best survey I know, 45% of burials were cremations. Sometimes the remains would be dug into graves, perhaps laid in a small (or large) boat or a wagon. Sometimes they would be placed on the earth and large mounds would be built over them, with either earth or stones. Sometimes the corpses would be weighed down with stones, as if to keep the dead from rising again (although we don't really know why). And sometimes you'd cut off the head of a loved one before laying their body to rest.

Perhaps you'd butcher some animals, maybe dogs, an exotic bird, and a horse. Perhaps you'd even kill a human being to accompany the dead—although this was extremely rare. And maybe you'd throw in other fancy things. Dress them up in fine textiles and glitzy jewelry. Put in all the objects that they used on a daily basis—spindle whorls, sickles, gaming pieces. Perhaps you'd drop in a few coins.

One thing archaeology tells us: These were weird people, and everybody did things differently. Just one glance through the cemeteries of the Viking Age tells us that these people had a vast variety of thoughts about death and what to do with the dead. These beliefs seem to have been constantly changing, moving, and being reinvented. Even within the same community, people could hold very different opinions and bury their family members in very different ways.

It's a good reason to doubt that people from Iceland to Russia saw themselves as a single people or professed a homogenous religion. Did some people think they needed to die with a sword in their hands? Probably. But was it a widespread phenomenon that could invite a historical explanation? I'm skeptical indeed.

TLDR It's a modern myth, perpetuated by TV. People during the Viking Age didn't hold a single set of ideas about death, and it's probably wrong to group them all together as if there were a homogenous 'Viking' culture spanning two hundred years and over 4000 miles (7000 km — from Canada to Kazakhstan).