It was originally established in the classic series that a Time Lord can regenerate only 12 times (giving 13 incarnations). Thirteen lives was the limit first mentioned in "The Deadly Assassin". However, it was also established that this limit could be circumvented, and in fact was artificially imposed. In "The Five Doctors", the Master was offered (but not actually given) a further cycle of regenerations, as the High Council of the Time Lords had the ability to renewed the cycle. In "Utopia", we saw that he later had been given a new cycle of regenerations during the Time War. Before this, the Master used various methods to obtain new incarnations, artificially extending his life (this was a major plot element of "Doctor Who", the 1996 TV movie).
It has been established, too, that there are ways of preventing regeneration, such as killing before regeneration has a chance to take effect, as seen in "The Impossible Astronaut", and in "Let's Kill Hitler" it was shown that some poisons could be used to kill a Time Lord without them regenerating. In that latter story, we also saw that regenerations can be given up by using the regeneration energy to heal someone else. In "Last of the Time Lords", the Master apparently dies after refusing the regenerate, however subsequent events in "The End of Time" render this questionable.
In "Death of the Doctor" (Sarah Jane Adventures story), the Eleventh Doctor stated that he can regenerate 507 times. This has been confirmed by the writer of the episode, Russell T Davies, as being a joke.
The 2013 episode "The Time of the Doctor" confirmed that the Doctor only had 13 lives, and that due to the hidden existence of the War Doctor, and due to the aborted regeneration seen in "Journey's End", the Eleventh Doctor was actually the thirteenth incarnation and therefore at the end of his lives. However, the Time Lords, utilizing the Time Crack, infused the Doctor with new regeneration energy, renewing his regeneration cycle and allowing him to change. His ultimate final number of regenerations remains now to be seen.