That's a big question at the moment. The last episode of the most recent series ended with a cameo of John Hurt, and a suggestion that he would be the Doctor - but it was implied that he would be somehow different from the others. Most of the audience took this to mean that John Hurt would be next in line after Matt Smith, but now it seems this may not be true.
A lot of actors are being discussed for the role. Among other ideas, it's been suggested that it's time for a change from the usual white male stars, and names including Helen Mirren and Idris Elba have come up. There is also a suggestion that a former companion could undergo a transformation and become a Doctor as well - so that could mean Jenna Louise Colman, the most recent, or even Billie Piper. However, none of these stories has been confirmed and Matt Smith still has a November episode and a Christmas special to go, so it will be a while before we know more.