Talking to my friends, you would be under the impression that the Vikings were the greatest warriors that ever lived. But myself and none of my friends can actually name a single battle that Vikings fought in. Actually I know about the Battle of Stamford Bridge.
So I'd like it if people could name a few key battles for me to study, where Vikings won decisively and other where the Vikings were defeated decisively. Overall, would you compare the Vikings to other major conquering forces like the Romans, or the Mongols in terms of massive success?
One of the most famous battles that the Vikings lost was the Battle of Edington in 878CE. In this battle, Alfred the Great the King of Wessex managed to decisevly defeat the Viking army, and resulted in the Viking's leader Guthrum offering his surrender to Alfred. This formalised the borders between the English in the south and the west of England, and the Danes in the East and the North.
For battles that the Vikings won, I'd look at Rollo (baptised as Robert I) who after a number of raids was given the duchy of Normandy in Northern France. This is especially important as it was his descendant William who led the Norman conquest of England in 1066.
It's worth briefly noting that while the Vikings did occasionally assemble large armies, this was not their typical modus operandi. They were predominately raiders whose great advantage was the mobility conferred by their longboats. They actively avoided pitched battles, which were rare, preferring instead to retreat with their loot at the approach of sizeable Frankish armies. The problem that the Vikings posed was not that they were warriors par excellence but that their mobility just made them very difficult to engage and defeat. In this it was only really the ships that differentiated the Vikings from any other medieval raiding of the time.
So while there are a handful of Norse victories on the Continent (Luneberg springs to mind) and a series of stinging defeats (Leuven, Thimeon, Asselt, etc), this doesn't really convey the persistent nature of the Viking threat. After all, only in Dublin and Normandy did the Viking polities last, and both of these were eventually folded into Irish and France kingdoms, respectively.
England was different from the above examples from Francia. Given the weakness of central authority and military strength of the English kingdoms, permanent conquest became an option in a way that it never really had been on the Continent. (Ditto for Russia but that I know little about.) Even in England Viking conquests eventually gave way to native resistance - while I can't comment too much on England, in Ireland the key victory over the Vikings came at Clontarf in 1014.
(Chris Wickham's Inheritance of Rome puts the Vikings firmly in the context of the broader European history.)