There are eleven Doctors on Doctor Who, right? Well, yes, but not exactly. Those are the "canonical eleven" — the official Doctors. But are you familiar with some of the others?
1. The Dalek Movie Doctor
In the mid-60s, Dalek Fever was sweeping England. Dalek creator Terry Nation secured the rights to produce two Doctor Who movies. The Daleks and Dalek Invasion Earth: 2150 AD starred legendary British actor Peter Cushing (famous for Hammer films and Sherlock Holmes, and later famous as Grand Moff Tarkin in the original Star Wars film). His Doctor was more affable than William Hartnell's, and was different in another crucial respect—he was human. In 2005, the revived series played homage to the movies by borrowing elements of the TARDIS console room set, including the police box doors visible on the interior.
The trailer for Dalek Invasion Earth: 2150 AD
2. The Other First Doctor
When the series turned 20 in 1983, it was decided to do a spectacular feature-length episode featuring all five Doctors. However, two were unavailable: Tom Baker had other commitments and William Hartnell had died several years before. Hartnell's role was crucial, and the decision was made, for the only time in the series' history, to recast a Doctor. They selected Richard Hurndall, who leaned towards Hartnell's later, softer seasons. Hartnell made a cameo, in the form of retransmitted footage from "The Dalek Invasion of Earth" as a cold open, the only cold open in the original series' history.
First part of The Five Doctors, special edition edit. Hurndall appears around 4:25.
3. The Eight Morbius Doctors
Time Lords have thirteen lives, right? Well, until 1976, that wasn't established, and it was presumed they could regenerate indefinitely. In "The Brain of Morbius," the Fourth Doctor battles a heinous Gallifreyan criminal named Morbius, who is now reduced to a brain forced to live in a hideous, cobbled-together body. During a mental duel, the Doctor's past lives appear: Jon Pertwee, Patrick Troughton, William Hartnell... and then members of the production crew: George Gallacio, Robert Holmes, Graeme Harper, Douglas Camfield, Philip Hinchcliffe, Christopher Baker, Robert Banks Stewart, and Christopher Barry. After the 13-life limit was established, these eight became non-canon.
This clip is from the end of the story, so view with caution. The past Doctors show up around 14:00.
4. The Other Fourth Doctor: The Stage Doctor
In 1974, Doctor Who arrived on the stage in a production called Doctor Who and the Daleks in the Seven Keys to Doomsday, in a plot very loosely based on a TV serial, "The Keys of Marinus." Actor Trevor Martin was cast in the role, as an alternate version of the Fourth Doctor. He reprised the role a few years ago for an audio drama version of the story that is presently available on CD from Big Finish Productions.
These posters are for the stage and audio play versions of the story.
5. The Comic Relief: Red Nose Day Doctors
"Doctor Who and the Curse of Fatal Death" was a charity production for the Red Nose Day 1999 telethon. The story followed the Ninth Doctor as he announced his retirement and intention to get married, much to the disgust of the Master (played delightfully over-the-top by Jonathon Pryce), who teams up with the Daleks to destroy their mutual foe. Hijinks ensue, and the Ninth Doctor, played by Rowan Atkinson, ends up burning through all of his remaining regenerations as Richard E. Grant, Jim Broadbent, Hugh Grant, and, lastly, Joanna Lumley.
The full-length, official YouTube release by Red Nose Day
6. The Shalka Doctor
To celebrate the 40th anniversary in 2003, the BBC decided to try something new: an animated, webcast series, fully intended to be canonical. The Ninth Doctor was cast as Richard E. Grant, and "The Scream of Shalka" was produced and broadcast. It was reasonably successful, but it was quickly overtaken by Russell T. Davies' effort to revive the series live-action and became non-canon.
Part one of "The Scream of Shalka"
7. The Valeyard
Season 23, "The Trial of a Time Lord." The Sixth Doctor is on trial, and his prosecutor is a mysterious and sinister fellow called the Valeyard. But the Doctor realizes that the evidence has been tampered with, and it is eventually revealed that the Valeyard is in fact a possible future incarnation of the Doctor, and he has been promised all of the Doctor's remaining lives if he can get a conviction. Played with malevolent grace by Michael Jayston, the Valeyard escapes at the end of the serial, never to be seen again.
The Doctor arrives on Gallifrey and meets the Valeyard, the Inquisitor, and his jury of Time Lord peers.
8. The Dream Lord
In "Amy's Choice," the Doctor, Amy, and Rory find themselves in a strange dilemma — a sadistic fellow called the Dream Lord, played by Toby Jones, appears in the TARDIS and explains they have to decide which of two scenarios are real, before they get killed in one of them. He turns out to be a manifestation of the Doctor's own unconscious, triggered by psychic pollen caught in the Time Rotor. Fans have since speculated that this is the part of the Doctor that could eventually become the Valeyard.
The Dream Lord appears and explains their predicament.
9. The Watcher
There's another not-quite Doctor on the series, and he appeared in "Logopolis," the dramatic conclusion to Tom Baker's tenure as the Fourth Doctor. In the distance, a curiously luminous figure is seen, watching silently and then disappearing, occasionally helping, but never speaking. Played by Adrian Gibbs, "The Watcher" is a transitional Doctor, sort of an advance version of Number Five who appears to assist in a time of great danger.
Fan-produced set of Watcher clips (not exhaustive) from "Logopolis"