I was reading about Vinland and the Norse Colonisation of Greenland, when I began to wonder: If the "Vikings" could make it to America, however briefly, and get to places like Byzantium in the East, did they go any further? I understand this is rather difficult, as sometimes the existence of artefacts of a particular culture in a region might just denote a sophisticated trade route, and Artefacts from Point A could reach Point C through Point B, without anyone from Point A actually seeing Point C. So my question is what is the furthest distance that we know of that a Norseman travelled from Scandinavia in the Viking Age, through written accounts preferably?
I'm aware that Viking suggests raiding. What I mean by Viking is simply anyone from Scandinavia pre-1100, including traders and explorers, although there was a lot of overlap between raiding, trading and exploring.
The furthest East would be the Caspian Sea and the North of Iran (see my comment with sources [here] (https://www.reddit.com/r/AskHistorians/comments/43gon8/are_there_any_records_that_the_vikings_reached/)). Given that at least one expedition was mounted all the way from Central Sweden, this is probably the farthest they ever travelled in a single raid. Northern Iran is closer to Scandinavia than l'Anse aux Meadows (but way further than l'Anse aux Meadows to Greenland, of course).
According to a recent study, the oldest known evidence for mice on Madeira, an island off the west coast of Morocco, can be carbon-dated to shortly before 1036. Madeira is an isolated ecosystem and remained uninhabited until Portuguese colonization ca. 1420—so where did these mice come from? Unexpectedly, their DNA points to Scandinavia or north Germany, i.e. these were "Viking mice."
There's a few records of Norse activity around Iberia: small but far-ranging raids recorded in 844, 859, and 861, the last of which got wrapped up into the mythology of Ragnar Lothbrok, and some renewed but sporadic raiding in the 960s and 970s. On any one of these raids, or perhaps even in an undocumented trip for raiding or trading, a ship could easily have been blown off course and been forced to land at Madeira.
These trips, however, seem to have been based out of Ireland, i.e. led by the so-called Hiberno-Norse. But Western Europe is—at least today—populated by a completely different species of mouse. So whoever carried these mice to Madeira, whether or not they traveled with one of these Hiberno-Norse expeditions, they most likely had an earlier stop-over in Scandinavia. Alternately, the mice might have jumped from a Scandinavian trader at the Dublin docks onto a neighboring warship.
Regardless, these mice, perhaps over the course of a few generations of their family, made the long migration from Scandinavia to Madeira, sometime near the close of the Viking Age. In sum, they traveled a straight-line distance of 2000 mi (3300 km). This is perhaps slightly longer than the 1900 mi (3100 km) traveled in Ingvar's raid from central Sweden to the Caspian in 1041. And it far exceeds the distance of 1200 mi (1900 km) traveled by Greenlanders to the St Lawrence estuary, where they picked up a sample butternut burl that they left behind at their L'Anse aux Meadows base camp around ca. 1000.
Bonus! If you've ever had Madeira wine, it's made on the Madeira islands, and Viking mice are part of the reason why Madeira has a great ecology for wine production. It was one of George Washington's favorites!
There is clear archaeological evidence that Vikings were at L'Anse aux Meadows in Newfoundland, Canada and historical evidence that they were in Byzantium (Istanbul). They were many places in between including down through what is now Russia (via river) and all along the Atlantic Coast of Europe.
One interesting addition is a viking woman named Gudrid Thorbjarnardóttir. She is also called Gudrid the Far-Traveler ("Vidforla" in Old Norse). She is referenced in both of the Vinland Sagas (The Saga of Eirik the Red and the Saga of the Greenlanders). She was born in Iceland, traveled to Greenland and then accompanied her husband, Lief Ericsson's younger brother and the son or Erik the Red, on a voyage to "Vinland," now known to be in Newfoundland. But that is not all. Later in life she is recorded as becoming very religious and making a pilgrimage to Rome and returning to die in Iceland. So a Viking woman evidently traveled between Newfoundland and Rome in her lifetime. The sagas indicate that the trip to Rome was overland through Europe and not all the way by boat. I think it needs to be said that not everyone considers the sagas literal truth, but it is not in any way inconceivable that individual Vikings traveled in their lifetimes between North America and Southern Europe.
Follow-up question: Were the Norse unusually well-traveled by the standards of their contemporaries? We hear about Vikings in Byzantium, for example, but is that just because we like learning about the Vikings, or because no one else from Western and Northern Europe ever got that far?
Do you mean the furthest they traveled in a "single leap" so to speak, or the furthest we have evidence of them reaching from some point in the middle of mainland Scandinavia? And do you mean as the crow flies or the longest route they would have traveled?