A Dutch Treat?
The great beneficiaries of a failure of the Norse to engage in 'extreme tourism' in (what we call) the Viking Age would have been the people who spoke various forms of Low German - the Anglo-Saxons, the Franks, the Frisians, the coastal Saxons and their kindred.
In Great Britain, the absence of the Viking distraction would have allowed the Anglo-Saxons to expand into Celtic enclaves. Thus, we might end up with an Anglegland that covered a much larger part (and perhaps even all of) the island. At the same time, the absence of Norse influence on the language would lead to a situation where standard English would sound something like a West Country accent on steriods. In other words, presenters on the ABC (Angelish Broadcasting Corporation) would sound like Tolkien's Gaffer Gamgee. (Though the word 'gaffer', which comes from the Norse 'afi', meaning 'grandfather', would not exist...)
On the Continent, the Low German peoples would be better able to expand to the north, depriving Denmark of much of its Scandanavian character and turning the Western Baltic into a Low German lake and providing Low German with a much better chance of becoming a major world language and the Hanseatic League a better shot at evolving into a proper nation-state. (The Norse who remained in Scandanavia might resist the Drang Nach Norden of the Low Germans, creating the rough equivalent of Wales in Northern Scandanavia. Alternatively, they might be absorbed into the Low German world.)
If the Low German world achieves critical mass in this way, then High German might remain confined to its Alpine home. Thus, as places like the Mark of Brandenburg are 'Germanized', they are absorbed into the Low German world rather than its High German competitor. Similarly, with Low German becoming a language of trade, diplomacy and culture, much of northern France might end up as part of Greater Dutchland. We thus might have ended up with a situation in which the two of the great powers of our nineteenth century - Prussian-led Germany and France - never happened.
While the Low Germans would be the big winners in a Viking-free world, other possible beneficiaries include the other Baltic peoples (the Finns/Ingrians/Estonians, the Lithuanians/Latvians/Old Prussians and the Wends), and the Romance-speaking people of southern France (Provence/Catalunia) and (though this is less certain) an Ireland that, having become the refuge for Gaels and Britons from Angleland, achieved 'Celtic consciousness' (and thus political unity) at a relatively early date.