He is an older version of the Eighth Doctor
Similarly: John Hurt is the REAL Ninth Doctor
Recent seasons/series have made a VERY big deal out of the fact that Eleven IS Eleven, and have thrown the number 11 out there whenever possible. Just in the past several episodes, Clara names Chapter 11 as her favorite in Summer Falls and names whiskey as the "Eleventh most disgusting thing ever invented." Supporters of the theory might defend it and say that Eleven would still be Eleven and Ten would still be Ten, because the Doctor said he was Something Else. But it seems like Steven Moffat, for whatever reason, wants us to know exactly where we are in the order of regenerations.
John Hurt is the pre-TARDIS-stealing Doctor
John Hurt is an aged version of the Human Tenth Doctor
If John Hurt is a human Tenth Doctor, then he probably wouldn't be in the actual Doctor's head as one of his faces. Also, what did he do that was so terrible that Eleven feels the need to hide it?
John Hurt is the Valeyard
But it is probably something else entirely.
Steven Moffat usually comes up with something no one can see coming. Arguments all over the internet are getting heated, even though no one really knows for sure, with the exception of the cast and crew. There are probably at least 100 more theories out there; what is yours?