Most depictions like this seem to be based on the account of Ahmad ibn Fadlan, a Muslim writer from the 10th century who spent a lot of time amongst the Rus and witnessed the funeral of a Scandinavian chieftain who died on a trading expedition. The chief is placed in a ship and it is set on fire but unlike many depictions the ship has been pulled up onto land and a barrow is built over it. This appears to have a pretty strong basis in reality, several ship burials have been found around Scandinavia, the British Isles and Eastern Europe. They weren't always burned, the Oseberg Ship for instance is extremely well preserved and one of the greatest finds of the Viking Age.

Another part of Ibn Fadlan's account that doesn't tend to make it into modern depictions is part of the ceremony involving the ritual intoxication, rape and sacrifice of a slave girl owned by the chieftain. It's probably a little dark for modern audiences.