Here we present the results of a systematic ab initio study of point defects in titanium carbide. The electronic and atomic structure for the metal and non-metal vacancies, interstitials, and antisite defects (including the split interstitial and split antisite conformations) is calculated within the generalized gradient approximation of density functional theory, using the projector augmented wave method as implemented in the Vienna Abinitio Simulation Package VASP. In many cases the symmetric point defect configuration is found to be unstable against a symmetry-breaking distortion via the Jahn-Teller mechanism. An enhanced stability of titanium dumbbells is obtained for sub-stoichiometric TiC1-x where the dumbbells form clusters with the carbon vacancies. Possible migration pathways for point defects and their clusters are explored in order to create a database of possible mechanisms of self-diffusion in TiC.