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
Born in 1920, Patrick Troughton went directly into an acting career and was undergoing formal training in New York City when World War II broke out. He returned to England and joined the Navy, where he had a decorated career before returning to the theater, gaining a reputation as a reliable and versatile character actor. In 1953, he became the first person to play Robin Hood on television and found a succession of television, film, and radio roles afterward before Innes Lloyd, the new producer of Doctor Who, approached him in 1966 about succeeding William Hartnell in the title role. He ended up playing the role as what series creator Sydney Newman called a "cosmic hobo," inspired partly by silent film star Charlie Chaplin — brilliant, a bit egotistical, and also a bit of a comedian. He'd sometimes play the recorder, a significant change from the First Doctor, who had no apparent musical talent, and it was during this era that the sonic screwdriver was first seen. After three years, he decided to move on, although he returned three more times to reprise the role, in "The Three Doctors," "The Five Doctors," and "The Two Doctors." He returned to his work as a character actor after his time on Doctor Who, working hard despite doctors' advice due to major heart problems. In 1987, he defied doctor's orders to stay in the country and recuperate and went on one more convention tour. He died on March 27, 1987, in Columbus, Georgia. (I actually saw him once, and got his autograph, earlier in the same U.S. tour. He seemed in good health, but, well, he was a very good actor.) Acting was in his blood; several of his children and grandchildren have gone into acting. The youngest of these is Harry Melling, whom Harry Potter fans know as Dudley Dursley.
3. Jon Pertwee
Born in 1919, and thus actually a year older than the man he would replace, Jon Pertwee was born into a family that already had a lot of actors in it. Like the first two Doctors, he joined the military in World War II; although his service wasn't as distinguished as Troughton's, he did acquire an interesting souvenir: he woke up one morning after a drunken shore leave to find a tattoo on his arm, which made a brief appearance in his debut episode of Doctor Who. After the war, he became known as a comic actor on stage, television, and film. When he heard that the part of the Doctor had become available, he inquired and discovered he was already on the shortlist, and ultimately was cast. He played the character as an action hero with an almost James Bond flair, wearing opera capes and driving souped up cars (including the spaceship-like Whomobile, which actually belonged to Pertwee himself, built on commission by a custom car builder). After five seasons, he departed the role. His career didn't falter afterwards, and in 1979 he found his second children's TV role in Worzel Gummidge. He returned to the part of the Doctor for "The Five Doctors." Like Troughton before him, he kept up the convention circuit, meeting with his fans frequently, and he died of a heart attack in Connecticut on May 20, 1996.
(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.)
4. Tom Baker
Born in 1934 to a Catholic working class family in Liverpool, Baker first tried a career as a monk, then joined the military, serving as an orderly in a military hospital, before settling on acting as his career. In the '60s, he was a part of the National Theatre company under Lawrence Olivier, and in 1971 broke into film as Rasputin in Nicholas and Alexandra. In 1974, producer Barry Letts cast him as the Doctor. His interpretation was as arrogant and egotistical as all his predecessors, and just as determined to do good, but more eccentric, often described as "bohemian." The Fourth Doctor is particularly famous for his ridiculously long scarf, which resulted from a miscommunication between costume designer James Acheson and the knitter hired to produce it; Acheson never specified a length, and bought far too much yarn, so the knitter just kept going until it was all used up. Baker performed the part for a record-breaking seven seasons before retiring from it. After leaving, he had a brief marriage to costar Lalla Ward (the Second Romana), but it fell apart when both realized they'd really fallen in love with the other one's character, not the actor—an occupational hazard, unfortunately—and they parted amicably. He continued working on stage and screen, and is still active.
5. Peter Davison
Born Peter Moffett in 1951 (he chose the stage name "Davison" because there was already a Peter Moffatt on the English stage), Davison began work at Nottingham Playhouse and got into television in 1975 alongside the woman who would become his wife, Sandra Dickinson. (Sci-fi fans will remember her as Trillian in the BBC TV miniseries version of Hitchhiker's Guide to the Galaxy; it was her idea to get Davison into a big rubber suit to play the Dish of the Day in the same series.) But his first really big break was the role of Tristan Farnon, a young country veterinarian, in All Creatures Great and Small. In 1981, he got his next big break when he was signed on to succeed Tom Baker as the Doctor. Only 29 at the time, he was the youngest to play the role until Matt Smith in 2010. His Doctor had his little quirks, but was much less eccentric than his predecessor, save for a stick of celery he wore on his lapel and a preference for cricket attire. He left after three seasons. He returned for non-canon productions and the very short charity special "Time Crash," opposite David Tennant as the Tenth Doctor, the only "classic" Doctor to appear on the new series. After Doctor Who, he starred in A Very Peculiar Practice, Campion, and a revival of All Creatures Great and Small, as well as an assortment of other roles; he is still acting. His daughter from his first marriage, Georgia Moffett, later appeared on Doctor Who as well, the first child of a Doctor to appear on the show, in "The Doctor's Daughter" as, well, the Doctor's sort-of daughter. And that led, in a roundabout way, to Peter Davison becoming David Tennant's father-in-law, but more on that later...
6. Colin Baker
Born in 1943 (and of no relation to Tom Baker), Colin Baker initially studied law with the intention of becoming a solicitor, but at 23, found a different calling and became an actor. He had a smattering of television roles before appearing on Doctor Who in 1983 as Commander Maxil, commander of the chancellory guards on Gallifrey in "The Arc of Infinity." This got him onto producer John Nathan-Turner's radar, and he was cast as the Sixth Doctor after Peter Davison's departure. His tenure as the Doctor was a difficult one, marred by the battle of the production team with BBC leadership who hoped to see the series die. His costume was wildly garish, and he even attempted to kill his own companion in a fit of madness. But Baker put everything into the part and, although fans are mixed in their opinion of his Doctor, it cannot be denied that he threw himself into it, creating a Doctor who underwent a substantial amount of character development in two seasons. Unfortunately, the BBC1 Controller, Michael Grade, had never been a fan of the program and, after the troubled season 23, "Trial of a Time Lord," Colin Baker was fired despite having a full series left in his contract. He remains enthusiastic about the series despite that, however, and has lent his talents to numerous fan-made and non-canon productions. Following his time on Doctor Who, he moved primarily into theater, but still does occasional film and television work as well.
7. Sylvester McCoy
Born Percy James Patrick Kent-Smith in Dunoon, Scotland, in 1943, Sylvester McCoy would become the first non-English actor to play the part. (To date, there has been only one other: Scottish actor David Tennant.) He never knew his father, who died in World War II shortly before he was born, and he was raised in Dublin, Ireland. He tried a variety of careers before joining a comedy/vaudeville act called "The Ken Campbell Roadshow." One of the parts he played was a fictitious stuntman named Sylveste McCoy; confused reviewers thought it was his actual name, and he eventually adopted it as a stage name (adding an "r" to the first name to make it look better). In 1987, Doctor Who came out of a year-long hiatus following the firing of Colin Baker, and Sylvester McCoy was cast as the Seventh Doctor. His performance was evocative of the Second Doctor, and clearly informed by his comedy background, but in his second season became increasingly dark. The series was indefinitely suspended in 1989, ending the bulk of his tenure, although he returned for the American-produced Doctor Who movie in 1996, to film a regeneration scene to transition to Paul McGann. Following his work on Doctor Who, he worked extensively in theater and radio; he was nearly Governor Swann in Pirates of the Caribbean and even more nearly Bilbo Baggins in The Lord of the Rings. He recently traveled to New Zealand to film the part of Radagast the Brown for The Hobbit.
8. Paul McGann
Born in Liverpool in 1959, Paul McGann would ultimately have the shortest tenure as Doctor. He was born to a large family, and all four of the McGann boys went into acting. He played a series of roles on television before landing one of the two title roles in Withnail and I, playing Peter Marwood, the "I" of the title who is never named in the movie itself. He performed in a number of films after that, including American films, and was cast as Richard Sharpe, but a football injury just after filming started meant the number two, Sean Bean, got the part instead, and McGann ultimately walked away with a two million pound insurance settlement to compensate for the lost work and career advancement. In 1996, he was cast in an attempted revival of Doctor Who, filmed largely in Vancouver, British Columbia, and set in San Francisco, which was intended as a "back door pilot." It received very good ratings in the UK, but failed to interest US studios. That was the end of that effort, but Paul McGann went on to pursue a respectable film and television career. Recently, he has recorded audio plays featuring the Eighth Doctor — the BBC does not consider these plays canon — including a "do-over" of "Shada," a story written and partially recorded for the Fourth Doctor's tenure, but that was left uncompleted due to industrial action.
9. Christopher Eccleston
Born in 1964 to a working class family in Manchester, Eccleston pursued an acting career right out of school. He broke into film and television in the early '90s, keeping very busy and receiving multiple awards for his work in television before producer Russell T. Davies cast him as the Ninth Doctor in a newly revived Doctor Who. He played the part in more ordinary dress than his predecessors and with his natural Northern accent. Eccleston was the first Doctor younger than the series itself (by a few months) and the first other than Hartnell to have never seen it prior to being cast. He studied "The Talons of Weng-Chiang" (a Fourth Doctor serial), which was then newly released on DVD, as preparation, and came up with a Doctor who was every bit as egotistical as his predecessors, mischievous and impulsive, but also shadowed with massive grief—sometime in the untransmitted interim, his race had gone to war with the Daleks, and he was now the only Time Lord left. He was also in some way responsible for the fact that the Time Lords were now extinct. He was only contracted for one season, due to uncertainty whether the BBC would even be interested in commissioning a second season; miscommunications with the BBC marred his departure, as he was mistakenly reported to have quit due to issues with the crew when, in fact, it had been planned that way from the outset. He resumed his intense schedule after Doctor Who and, in 2011, earned the International Emmy Best Actor award for his role in Accursed.
10. David Tennant
David McDonald was born in 1971 in West Lothian, Scotland, later taking the name David Tennant as his given name was already in use by another performer. He was a born Whovian, and at the age of three announced his intention to go into acting because of it. A precocious actor, he managed to enter the Royal Scottish Academy of Music and Drama at 16. He performed a variety of roles, including many with the Royal Shakespeare Company, and began breaking into television in the 2000s. In 2005, he appeared in Harry Potter and the Goblet of Fire as Barty Crouch, Jr., and appeased his inner Whovian by appearing in the Big Finish audio productions that sort of worked around the edges of Doctor Who continuity and in the abortive attempt at an online animated series, The Scream of the Shalka. He achieved his lifelong dream in 2005 when he was cast as the Tenth Doctor. He elected not to use his natural Scots accent for the part, affecting an Estuary accent, and played it a more confident and more vengeful Doctor than Eccleston. During his first season, he became the first Doctor to appear with someone from the classic series, when Elizabeth Sladen reprised her role as Sarah Jane Smith in "School Reunion." That prompted a spinoff series called The Sarah Jane Adventures, and he appeared in an episode of Season Three of that show. He also provided voice work for two animated series, The Infinite Quest and Dreamland (the latter of which was referenced twice on The Sarah Jane Adventures). After three full seasons and a series of one-off specials in 2009, Tennant left the series, saying that he had to leave while he still could; any later and he wouldn't be able to bring himself to quit. After leaving the series, he became engaged to actress Georgia Moffett, Peter Davison's daughter. The two have since married and have a daughter together.
11. Matt Smith
Born in 1982 in Northhampton, Matt Smith initially dreamed of becoming a professional football player. ("Soccer" to us Yanks, of course.) A back injury put a stop to that, and his drama instructor at school pushed him into acting. He began to study drama and creative writing. He appeared in a variety of stage and television roles, but it was a complete surprise to most when he was cast as the Eleventh Doctor, the youngest ever to take the part. Producer Steven Moffatt had been going for someone in his mid-40s, but was particularly taken by Smith's oddball demeanor and ability to look very old indeed. His Doctor was played as an absent-minded professor, complete with tweed jacket and bowtie (which he obliviously insists is cool), with a sometimes mercurial disposition. He has also appeared on The Sarah Jane Adventures and has provided voice work for a series of video games. He has been signed for an additional 14 episodes, so will be the Doctor for at least three seasons. Like Eccleston, Smith was largely unfamiliar with the series before accepting the role, but he had an excuse—he was only seven when the series went on hiatus. (And now some of us can start feeling old!)