As of 2015, there have been 13 Doctors, not including the Valeyard, the meta-crisis Doctor, or any other in-between, duplicate, or other such alternate or illegitimate Doctors.
The numbering of the Doctors has become out of step with the number of incarnations. For the first eight incarnations, they were the same. During the Last Great Time War, however, the Eighth Doctor regenerated into an incarnation -- usually known by fans as the "War Doctor" -- that didn't call himself "Doctor", though others did use that name for him (see "The Night of the Doctor"). He in turn regenerated into the Ninth Doctor, who was the tenth incarnation of that Time Lord (see "The Day of the Doctor").
To complicate matters still further, the Tenth Doctor (eleventh incarnation) regenerated once without changing his body (see the end of "The Stolen Earth" & the start of "Journey's End"). Depending on how you choose to count incarnations, therefore, the Tenth Doctor was either the eleventh incarnation or the eleventh and twelfth incarnations, making the Eleventh Doctor either the twelfth incarnation or the thirteenth.
On top of all that, the Time Lords granted the Eleventh Doctor (an unspecified number of) further regenerations & he used one to become the Twelfth Doctor (see "The Time of the Doctor") -- either the thirteenth incarnation or the fourteenth, depending on how you count them.