One of the things that makes this a difficult question to discuss is that the question "Was Ragnar Lothbrok historical?" is itself somewhat ambiguous. Thus, before the question can be discussed, the question has to first be more clearly defined. To mention two opposite extremes, a skeptic could ask whether or not everything which is said about the character of Ragnar Lothbrok is historically accurate, observe that the answer is certainly "no", and then claim victory. At the other extreme, a proponent of a historical Ragnar Lothbrok could ask if a Viking by the name of Ragnar ever existed, point out that a Viking having the correct name ("Reginheri") appears in the Frankish annals, and claim that Ragnar Lothbrok was therefore historical. Neither of these two extremes is acceptable in a serious argument on the subject, so I will discuss the subject from the following middle ground. The criterion which I will use are that in order for Ragnar Lothbrok to be considered as historical, there should be a historically documented person of that name who actually performed a significant number of the deeds attributed to the legendary Ragnar Lothbrok. I think this is a reasonable criterion, since it places the burden of proof where it belongs, i.e., on the shoulders of those who claim Ragnar Lothbrok to be historical. The remainder of this discussion is based on these principles.
Now, to answer the question: No, Ragnar Lothbrok does not appear to be a historical figure, based on the above criterion. I will give some comments as to why I have this opinion, and then mention some reading material for those who want more.

The contemporary historical records of the ninth century (when Ragnar Lothbrok supposedly lived) show only one Viking of the correct name, a Viking named "Reginheri" (a Latin form equivalent to the name Ragnar) in France who died in the year 845, according to the contemporary Frankish annals [Annales Bertiniani, or the Annals of St. Bertin]. The emphasized words in the previous sentence are often conveninetly overlooked by those who wish to use Reginheri as a historical prototype for Ragnar Lothbrok. Since Reginheri died in France in the year 845, he cannot have participated in the later events which form the principal part of the legendary Ragnar Lothbrok's exploits.
In addition, there is no good evidence that Reginheri was the father of any of the individuals who later came to be regarded as sons of Ragnar Lothbrok. Thus, Reginheri fails to satisfy the criterion mentioned above. No other historical Norseman named Ragnar is known for the appropriate time period.

No contemporary record gives this name, and it is significant that when the name finally does make it appearance in the records 200 years later, it stands alone. (Ari, writing in the twelfth century, was the first known writer to make Ragnar and Lothbrok the same person.) The name first appears (as "Lothbroc") in "Gesta Normannorum Ducum", by William of Jumieges, writing about 1070, in which Lothbroc is called he father of Bjorn Ironside. (A Viking named Bjorn is verified by the contemporary chronicles, but without the nickname.) Adam of Bremen, writing soon afterward, called Ivar the son of "Lodparchus". Besides the fact that this Lothbrok is not attested in any of the contemporary sources, there is another potential problem, and that is that the name ("Lothbroka") might be a women's name. See the article on "Ragnars saga" by Rory McTurk in "Medieval Scandinavia: an encyclopedia" (New York and London, 1993). If this argument based on philology is correct, then this Lothbrok(a), if historical at all, would be a women, and clearly not identical with the legendary Ragnarr Lothbrok. (I do not have the background in linguistics to comment further on this gender argument.)

The "Fragmentary Annals of Ireland" (edited and translated by Joan N. Radner, Dublin, 1978, formerly called "Three Fragments") has an item of interest which has frequently been pointed out as possibly relating to the legend of Ragnar Lothbrok. In it, a certain Ragnall (Rognvald) son of Alpdan (Halfdan), king of Norway, is mentioned, and his exploits prior to the fall of York to the Danes are given, in a context in which it is at least arguable that Ragnall and Ragnar Lothbrok were the same person. There are two problem with this interpretation. First, Ragnar and Ragnall are not the same name, even though they look similar. Second, and more important, the Fragmentary Annals are themselves not a contemporary source, and there is good reason to be suspicious about them.
However, even if we were to allow that the events given there are historical (a concession which many historians would be unwilling to make), and then concede further that these events form the basis of the Ragnar legend, then we would still have that the person on whom the legend was based did not have the right name.

We have already seen that the only historically attested Ragnar (Reginheri) cannot reasonably be regarded as a historical prototype for Ragnar Lothbrok. Thus, it appears that the best attempt to argue for a historical Ragnar Lothbrok is to propose (as has been done on numerous occasions) that Ragnall and Lothbrok were both the same person, and then assume that the similar (but different) names Ragnall and Ragnar were accidently confused. In his article "Ragnarr Lothbrok in the Irish Annals?" [Proceedings of the Seventh Viking Congress, 1976, pp. 93-123], R. W. McTurk approached the problem from the viewpoint of looking in the statements made in the sources, and seeing what assumptions would have to be made about those statements in order for us to accept a historical Ragnar Lothbrok who was a member of the Danish royal family. In my opinion, his requirement that Ragnar should be a member of the Danish royal family is not really needed in order to argue for Ragnar Lothbrok's historical existence, and this requirement led to a long discussion of the genealogical relationships of the early Danish kings (not always convincing) which were not of immediate relevance to the question of Ragnar Lothbrok's historical existence. Thus, I am going to approach the problem in much the same way as R. W. McTurk did, but without making any requirements about the genealogical origin of Ragnar Lothbrok. Thus, suppose we were to assume that Ragnall and Lothbrok both existed and were the same person, from which it could then reasonably be assumed that man named "Ragnall Lothbrok" existed (later misnamed "Ragnar Lothbrok" by a minor error in the Icelandic sources). If, as a thought experiment, we claim that this is the case, then there appear to be six assumptions which are necessary and a seventh which is highly desirable:

1. We must assume that Adam of Bremen (late eleventh century) was correct in giving "Lodparchus" (i.e., Lothbrok) as the name of the father of Ivar (late ninth century).
2. We must assume that the "Coghad Gaedhel re Gallaibh" ("The War of the Gaedhil with the Gaill", ed. by Todd, London, 1867), a twelfth century Irish source, is correct in stating that Halfdan of Dublin (killed in Ireland in 877, according to the Annals of Ulster) was the son of a certain Ragnall, and that this Ragnall was the same as the Ragnall who appears in the Fragmentary Annals of Ireland.
3. We must assume that the Anglo-Saxon Chronicle is correct in stating that a brother (unnamed, but called Ubbe in later sources) of Halfdan and Ivar was killed in England in 878, despite the contradictory testimony of Aethelweard which gives a very different reading for the same event (see 4).
4. We must assume that the chronicle of Aethelweard is wrong in stating that Halfdan brother of Ivar was killed in England in 878, for otherwise that would prove that Halfdan of Dublin (d. 877 in Ireland) was a different person from Halfdan brother of Ivar.
5. In addition to assuming that Halfdan of Dublin was the same person as Halfdan brother of Ivar, we must also assume that this Ivar was the same person as Adam of Bremen's Ivar, keeping in mind that Aethelweard's chronicle, if correct, would imply the existence of two Ivars in the British isles at this time.
6. We must assume that the philological argument making Lothbrok(a) a feminine name is incorrect.
7. If Ari, the earliest author to mention Ragnar Lothbrok, is to be considered a reliable source on this matter, then we must also assume that Halfdan of Dublin was the same person as the Halfdan brother of Sigifrid who appears in the Annals of Fulda for the year 873, despite the severe chronological problems which that would cause with Ari's genealogies.

Since all of the above attempts to find a historical Ragnar Lothbrok fail to satisfy the mentioned criteria, Lothbrok and Ragnall come from noncontemporary sources which are themselves open to suspicion, and the historical records show nobody else (as far as I know) who could be plausibly identified with Ragnar Lothbrok, it must be concluded that Ragnar Lothbrok is not historical according to the terms described above. In fact, if there is any historical basis to Ragnar Lothbrok legend, it is quite likely that Ragnar Lothbrok is the result of combining two or more distinct individuals into a single character having the attributes of both, in much the same way as Ragnar Lothbrok's legendary "father" Sigurd Ring is in fact a composite of two different men who fought against each other for the Danish throne in the year 814, Sigifridus ("Sigurd") and Anulo (of which "Ring" is a translation of Latin "Annulus"). However, such composite characters cannot be considered as historical, and there is no evidence which comes close to being contemporary which shows that either Lothbrok or Ragnall existed.

The most ambitious attempt to portray Ragnar Lothbrok as a historical figure is "Scandinavian Kings in the British Isles 850-880" by Alfred P. Smyth (Oxford University Press, 1977). For a very critical examination of Smyth's views, see "High-kings, Vikings and other kings", by Donnchadh O' Corrain, in Irish Historical Review, vol 21 (1979), pp. 283-323 (very highly recommended). Both of these sources cite numerous other relevant sources for those who are interested in further details.

[Note: The usual apologies if my transliterations from the Old Norse alphabet into the alphabet available to me is a bit sloppy.]

Stewart Baldwin