No, Ragnar Lothbrok (the main character in the television series Vikings, in case anyone is wondering why this question is being asked) did not exist. There is no surviving material evidence that supports the claims of his existence made by several 12th century Scandinavian poems and a Danish chronicle. Ben Waggoner, in his introduction to his translations of a few of these poetic epics, notes that Icelandic sagas usually follow genre conventions that romanticize the 9th century Vikings as founders of what was to become the 12th century Scandinavian states and often drew from previous or contemporary literary traditions without much attention paid to historical accuracy. The Gesta Danorum, a chronicle written in the 12th century by a Danish ecclesiastical figure, places Ragnar in a very distinct historical context and associates many important contemporary figures and events with him. This chronicle is the most convincing piece of evidence for Ragnar's existence. However, the range of Ragnar's achievements and kin as described in the text are dubious, and are unsupported outside of those aforementioned sagas dedicated to him, which themselves are dubious.

So in short the Ragnar Lothbrok we know and love is either a completely invented person or a Frankenstein of other historical figures.

There is indeed a lot of conflicting information on the matter, mainly because the scandinavian peoples didn't have a habit of writing annals of events or other useful primary sources that would be relevant here. As such, there's only two contemporary sources (that I am aware of.)

First is the Anglo-Saxon Chronicle that details at least some of the activities ascribed to Ragnar Lothbrok, but it doesn't consistently name the Heathen/Danish leader (though it does mention a Haelfdan as a Danish King and consistently refers to him after that point as a leader, it's reasonable to infer that he may not have been the leader prior to this first mention, and this is likely referring Halfdan Ragnarsson.)

The actions and movements of unnamed leather of these Heathens/Danes prior to Haelfdan's appearance in the text do appear to align with what we know of Røgnvaldr/Ragnall ui Ímair (same person, different language.) A viking king with significant power in the British Isles.

Second is the Ragnarsdrápa, a skaldic poem attributed to a contemporary poet (and this does not appear to be an unreasonable attribution) however it is not clear this poet is talking about the same Ragnar, and the poem has not fully survived, with the only parts we know being subsumed into the prose edda (which was composed significantly later.)

Other medieval sources were produced significantly later and are heavily laden with mythic elements, as such they are of limited value on whether or not Ragnar Lothbrok existed. However, they do provide a clear sign that the tale of Ragnar Lothbrok was persistent.

That said, this evidence does not by itself lend itself to a clear picture on the matter, and several of the actions ascribed to Ragnar Lothbrok seem to be based on the actions of multiple, different Viking kings. However, I believe there is sufficient reason to believe Ragnar Lothbrok is at least based on a historical Viking king and that later historians and saga authors seem to have conflated this particular king with other Viking kings of the time, in addition to the common embellishments of the kind of mythologizing that the Sagas tend to do.

Thank you very much, to both of you. :)