I've often pondered such a scenario. One convoluted and vague timeline would involve a pre-Viking Age POD wherein Christianity fails to fully take hold in Anglo-Saxon England.
The idea is that if we assume the Norse desire for wealth and living space was the result of pressures that will exist no matter the timeline, then they will still raid Northern Europe. Let's then assume that the conquest of England still goes ahead, but this time England is home to a substantial pagan population. Though Anglo-Saxon pagaism was not identical to Norse paganism, from what little we know the two were similar, and in any case pagan religions didn't tend to be overly discriminatory to other pagan religions.
This gives the Norse ruling class a stronger base and less pressure to Christianise. If they successfully subsume England, given enough time that creates a powerful pseudo-Scandinavia state primed to retain a culture of seafaring. As naval technology progresses (they might even lead the charge on that front) the Anglo-Norse can raid farther. We might very well see earlier permanent settlements in North America that aren't doomed to fail.
So what next? Let's say the Reconquista still occurs in Iberia. Religious fervour is high in Europe and the pagan north is feeling isolated. Raiding for resources and wealth resumes. We get a blend of a Second Viking Age and a Golden Age of Piracy. If we also assume some Christian power still makes first contact with Mexico, the Caribbean, the Inca, and so on, we could see pagan pseudo-Vikings/privateers raiding the Atlantic out of secret bases in the Caribbean, Africa, and North America.
As I said, convoluted, but fun to imagine.
