I just spent a semester studying this! Well, not only Arthur's historicity, but many of the medieval (and more modern) retellings as well.
I agree with what SW said above. There was a mention of an Arthur in several of the 5th and 6th century chronicles, but so few of these actually survive, and much of what has survived came from later recopyings (is that a word? probably not).
Scholars have spent much time looking at the archaeological remains from this period, and have indeed found a stone at Tintagel which is inscribed with PATER COLI AVI FICIT ARTOGNOV. The British version of the Latin "Artognov" is "Arthnou," which contians the same Celtic root as "Arthur" ("bear". This is just one of several pieces of archaeological evidence that historians have used to justify the existence of someone famous named Arthur, but this has by no means been proven.
It will likely never be known for certain whether a sin gle "historical" Arthur existed. If he (or they) did, as mentioned in other posts above, it is almost impossible that he was the sort of figure that exists in most of the retellings today. Because, also as mentioned above, most of the other characters that we known today were added in to the story at a much later date.
Is an eyeball in an eagle's talon as good as an eyeball on its own?