Most historians dismiss him as unhistorical at this point, but there are those of us who hope he turns out to be a real character. We have some new help from The History of English podcast, which discusses the possibility from a linguistic point of view in its 30th episode.
The new thought is that Arthur does not appear by name, even though their are references to a great leader defeating the Saxons at Mount Badon not long after the supposed event, because Arthur was actually a title, meaning High King. Arda- Rik. Apparently the Irish and Scots still use Ard-Ri with the same meaning in some contexts. This is further supported from the name of one of the proposed Arthurs, a "King of the Britons" called Riothamus (c. 440-500) who also fought in Gaul and was important to the Bretons. That name also means "high king," though the elements are reversed, with the "Rik" (related to rex, reich, rich, regal) coming first, Rigo- Tamos. So the actual Arthur could well have had another name, but in being referred to as the High King, that title stuck as a personal name.
Well, it could be true. I admit we are bitter clingers at this point, but cling we shall.