The world’s longest-running science fiction television series ran from 1963-1989 and then returned in 2005, after a gap of about nine years after the release of the Fox Network TV movie that introduced Paul McGann. The new series is still going on, and will hopefully continue for some time to come.
The new series varies in format and content from the classic, although the Doctor retains his quirky personality, his preference to solving problems with cleverness as compared to guns, and his penchant for picking up companions. During the centuries between the old and the new, we’ve learned that there was something called the Time War, which involved old nemeses the Daleks and resulted in the destruction of the entire Time Lord race - except for the Doctor. However, in "The Day of the Doctor," the Doctor learns that his race is not dead, only hidden away, and it sounds like he will set out to find them.
The classic series was often introduced to American viewers weeks or months after an episode aired in the U.K. These days, thanks to current technology and the Doctor's worldwide popularity, the delay is negligible; some episodes, such as the recent 50th anniversary episode “The Day of the Doctor,” are simulcast. That episode was also shown in theaters around the U.S.
on November 25, 2013 (and in 11 select American cities on November 23, when the show aired for the first time). Episodes are an hour long now, and the show's first run in the U.S. takes place on BBC America.
To date there have been five men playing the role of the Doctor in the new series: Christopher Eccleston, David Tennant, Matt Smith, Peter Capaldi (he took over Christmas 2013, and John Hurt (known as the War Doctor, and not strictly numbered). Although at this point we don't know how old the Doctor is, it appears that our real-time years between 2005-2013 have spanned at least 400 or 500 years in the Doctor's life. The number is possibly much higher now; Clara put the Doctor's age in the 2000s during a ninth season episode, which is several hundreds more than what was revealed during the 50th anniversary episode.
Several of the classic Doctors have been featured in bonus material over the course of the new series - Paul McGann appeared in a six-minute prequel to “The Day of the Doctor,” and Peter Davison, who is now David Tennant’s real-life father-in-law, was in a short “Children in Need” special with Tennant called "Time Crash." Also, Peter Davison, Sylvester McCoy, and Colin Baker starred in a short video playing themselves run amok on the set of the 50th anniversary special, "The Day of the Doctor." The fourth Doctor, Tom Baker, was featured in the special itself.
As before, the show is about a Time Lord from Gallifrey who travels the universe trying to stop the worst abominations. He “regenerates” when he dies - and although, in the classic series, it was said he had a limited number of regenerations - 13 to be exact - he's now past his allotted generations in the new series, and the reasons why are a bit murky (David Tennant's Doctor apparently regenerated into himself again at some point). During his travels he has encountered both new and old enemies and allies.
And he’s picked up companions, both male and female, who appear to have more flexibility in returning home and contacting loved ones than the old companions did. These companions’ families are often involved in stories, which didn't really happen in the classic series (except possibly in stories that introduced the companions).
The 9th Doctor (Christopher Eccleston,2005): The Ninth Doctor is a darker, less frivolous, brooding version of his previous self, having lived through the Time War, but still with the friendly, intelligent personality of the Doctor in all his incarnations. His companions included Rose (Billie Piper), Rose’s mother Jackie, Rose’s ex-boyfriend Mickey (Noel Clarke), one-shot Adam Mitchell, and Captain Jack Harkness (John Barrowman. Allies included Harriet Jones, and enemies that he encountered included the Slitheen, Lady Cassandra, the Gelth, the Mighty Jagrafess, and Daleks.
Catchphrases included "Fantastic!" and "Oi!"
The 10th Doctor (David Tennant, 2005-2010) - The Tenth Doctor was more outgoing and lively than his predecessor, choosing to wear a long trench coat over Converse sneakers. Many consider this incarnation of the Doctor to be their favorite; he is younger than all the previous ones. His companions included Rose Tyler, her family, Martha Jones (Freema Agyeman), Donna Noble (Catherine Tate) and several one-shots such as Wilfred, Donna's grandfather (Bernard Cribbins), and River Song (Alex Kingston). Enemies encountered included the Krillitane, the Family of Blood, The Weeping Angels, the Master and Adipose. This doctor had more one-shot companions than most, in part because during one year, producers chose to air a series of specials rather than a regular 13- or 14-episode season, and he did not retain the companions of those specials. Catchphrases included "Allons-y." He was the Doctor who said, "People assume that time is a strict progression of cause to effect, but actually, from a non-linear, non-subjective viewpoint, it's more like a big ball of wibbly-wobbly...timey-wimey...stuff." This came from the episode "Blink," often considered to be the creepiest episode of the new series.
The 11th Doctor (Matt Smith, 2010-2013) - The Eleventh Doctor, played by the youngest actor of the bunch (he is three years younger than Peter Davison was when he took on the role), is a more childlike and endearingly goofy Doctor - but also harder in some ways, and more manipulative. He likes soccer, thinks hats are cool, and uses "Geronimo" as one of his catchphrases. He has been known to eat fish fingers with custard and to have a lemonade tap put into a house. His companions have been Amy Pond (Karen Gillan), Rory Williams (Arthur Darvill), and Clara Oswin Oswald (Jenna-Louise Coleman). Enemies he has encountered include Madame Kovarian, the Atraxi, the Great Intelligence, and the Silence. This Doctor has also visited his own final resting place at Trenzalore.
The 12th Doctor (Peter Capaldi, 2013-Present) - The Twelfth Doctor is older, thinks hugs are a way of obscuring your face from your friends, and is a touch more irascible than the previous doctor, but he has so far received a good reception from audiences, though the quality of episodes in his first season was mixed. He is going into his 10th season as of this writing. His lone companion to date is Clara (Coleman), who wasn't sure if she'd stay with this doctor. He also came into contact with Danny Pink (Samuel Anderson), Clara's boyfriend.
There's a lot more to the show - it's difficult to encapsulate 50 years of a show in one article, but these are the basics regarding the Doctor.