Time Lords have 13 lives, their original plus 12 regenerations. However in the episode "The Five Doctors" the Timel Lords offered to give the Master (who had used them all up) a full set of new lives if he helped them, so there is a way for the Doctor to acquire new ones if need be. William Hartnell is the first Doctor. Paul McGann is the ninth and appears to be generally regarded by the people who do books and websites on the subject as a bona fide incarnation: he appears in definitive lists and novels and suchlike. Peter Cushing on the other hand does not count because his films were all remakes of William Hartnell TV stories so he was only playing the first doctor, not a regeenration in his own right.
Everybody got that? Good!
Everybody got that? Good!