Heaps of liberties are taken. That said, one famous historical Viking is said to be the son of Ragnar, and I suspect it will be the child that Ragnar's girlfriend is currently carrying.
My gripes about the historical inaccuracy were threefold.
1. The depiction of Viking government as autocratic rather than council-based, which, in turn, had an impact on the depictions of Viking law. They changed this SOLELY to show a traditional "medieval" power struggle between a lord and an upstart, and it was just crap. Total crap.
2. The mixing up of VERIFIABLE dates in history, like the raid on Lindisfarne and the ages of King Aella of Northumbria and Ragnar, both in relation to that, and in relation to each other. Again, done just so they could show some particular moment in history, and to create more "villains vs. heroes" drama.
3. The apparent ignorance of the existence of the British Isles by the Vikings. The Vikings were WELL aware of the existence of the British Isles, particularly when Ragnar was alive, HAVING ALREADY RAIDED LINDISFARNE WHEN RAGNAR WOULD HAVE BEEN A BABY. Again, done PURELY to create a sense of "Oh look! Intrepid Viking explorers!"
My complaints about these issues are that they are gross deviations from history, done purely to create the most rote form of drama, and -- more importantly -- they're totally unnecessary to create an interesting story. I don't mind that they establish some fictional enmity between Ragnar and the local Jarl, but they were just
lazy in depicting the mechanisms by which that play out as essentially due to tyrannical autocracy rather than, say, manipulation of the local democratic/council institutions (the Thing). I mean, come on. House of Cards is wildly successful. Surely you can write a story -- even set in the Dark Ages -- that depicts similar machinations AND which shines an interesting light on Viking culture. Same with the rivalry between Aella and Ragnar. Although it existed, there's no reason why you have to make Ragnar the young upstart. You could also show a different random raid on a monastery (they did continue for quite a while) even without it being THE raid recorded in the historical record. And there's just no reason to show Ragnar as both an explorer and a warrior. There's plenty of drama involved in making the crossing from Scandinavia to the British Isles in longships without resorting to "And these are the first Vikings to EVER LAND!!" nonsense. Hell, make it so that Floki is simply unsure of the precise passage and none of Ragnar's guys have ever gone raiding to the British Isles so it's all new TO THEM, rather than TO ALL VIKING CULTURE.
Simple things like this would preserve the historical accuracy of the show, while still making things interesting and exciting, but the show was too busy being lazy and stupid to do that. I don't care if their clothes don't look perfectly right, or if the rudder is on the wrong side of the longship or whatever. What I care about is that the show just...couldn't be arsed to bother writing anything by a paint-by-numbers medieval drama and then shoved that -- historical inaccuracies be damned -- into a Viking setting because it assumes its audience is a bunch of morons with zero interest in history.