There have been many actors who have portrayed the Doctor in various settings, but eleven have been the official Doctors. We'll look at all of them here.
1. William Hartnell
Veteran character actor William Hartnell was born in 1908 to humble beginnings; his mother was unwed, he never knew his father, and his first career move was into petty crime. A boxing instructor got him started on horse racing, but he found his real passion when he got a job as a stagehand at the age of 18. He quickly got into acting, working constantly with only a break to serve in World War II in an armored regiment. He ended up typecast in comic tough-guy roles (you can see one of them in The Mouse That Roared), and when Verity Lambert offered him the part of a mysterious time traveler in an educational show aimed at children, he jumped at the part. He created a character who was highly intelligent but not always as wise as he thought himself, brilliant but forgetful, cantankerous but with a deep compassion under the surface. He enjoyed the role tremendously, but by 1966, his health was deteriorating due to arteriosclerosis and he had to quit. The producers came up with the idea of having his character transform into a new actor, and Hartnell suggested Patrick Troughton, who was approached and accepted the part. Hartnell reprised his role once more for the tenth anniversary special, "The Three Doctors," but his health had deteriorated more than the production crew realized and his part had to be rewritten to accommodate his capabilities; it was his final work as an actor, and he passed away in 1974 at the age of 67.
2. Patrick Troughton
3. Jon Pertwee
(One odd coincidence—Pertwee's godfather was the actor Henry Ainley, whose son Anthony later took on the part of the Master, originated by Roger Delgado during Pertwee's tenure.)