I was recently writing a technical publication, and it's a bit of a tradition to "sneak in" references to something in the technical examples throughout the book. So this year being the 50th Anniversary, I thought I'd put in the names of actors to have somehow performed the role of the Doctor in a BBC licensed production. So not just restricted to "canon" but to any other licensed production of a Doctor Who story (so I decided to draw the line at Doctor Who skits in none Who shows, I also decided not to include stunt doubles and stand-ins).
I was quite surprised when I got through the list just how many they were, and I'm sure I haven't got them all yet.
Here's what I have so far -
Actual canon Doctors in the TV show itself-
1st Doctor - William Hartnell, Richard Hurndall (in The Five Doctors)
2nd Doctor - Patrick Troughton
3rd Doctor - Jon Pertwee
4th Doctor - Tom Baker
The Watcher (interim 4th/5th Doctor) - Adrian Gibbs
5th Doctor - Peter Davison
6th Doctor - Colin Baker, Sylvester McCoy (in Time and the Rani)
The Valeyard (distillation of the Doctor between 12th and Final incarnation) - Michael Jayston
7th Doctor - Sylvester McCoy
8th Doctor - Paul McGann
9th Doctor - Christopher Eccleston
10th Doctor - David Tennant
11th Doctor - Matt Smith
The Dreamlord (dark part of the Doctor, possibly proto-Valeyard) - Toby Jones
Disowned Doctor - John Hurt
12th Doctor - Peter Capaldi
Canon "fake" Doctors in the TV show (where another actor partly assumes the role of the Doctor)
5th Doctor - Ian Collier, Omega assuming the 5th Doctor's form, but speaks with Omega's voice
6th Doctor - David Collings, Mawdryn pretends to be a regenerated 5th Doctor (and then goes on to be an alternate Doctor for Big Finish)
DVD only Doctors - For the official DVD release of Planet of Giants a reconstruction was made to reconstruct episode 3 into it's original planned 2 parts. For this John Guilor provided the voice of the 1st Doctor for the missing scenes.
Dalek Movies (not Canon but officially licensed)
The Scream of Shalka (originally canon then retconned out)
9th Doctor - Richard E Grant
The Curse of Fatal Death (a non canon but licensed full length spoof)
9th Doctor - Rowan Atkinson
10th "Cute sexy and lick the mirror handsome" Doctor - Richard E Grant (again)
11th Doctor - Jim Broadbent
12th Doctor - Hugh Grant
13th Doctor - Joanna Lumley
An Adventure in Space and Time (a docu-drama about the programme) -
1st Doctor - David Bradley
2nd Doctor - Reece Sheersmith
3rd Doctor - Mark Gatiss (rumoured cameo)
4th Doctor - Steven Moffatt (rumoured cameo)
Officially licensed Stage plays
The Seven Keys to Doomsday - Trevor Martin (?th Doctor but ran between Pertwee and Baker)
The Ultimate Adventure - Jon Pertwee (3rd), David Banks (?th Doctor when Pertwee fell ill), Colin Baker (6th)
Big Finish (non canon but licensed Doctor Who audio dramas)
Doctor Who Unbound (Alternate Doctors) - Geoffrey Bayldon, David Warner, David Collings, Michael Jayston, Derek Jacobi (as far as I'm aware the only actor to have played both the Doctor and the Master in licensed productions), Arabella Weir.
Companion Chronicles many companions get to "fill in" the Doctors lines but as their character impersonating the Doctor whilst retelling the story, so probably not a true playing of the Doctor.
Light at the End (50th Anniversary special)
1st Doctor - William Russell
2nd Doctor - Frazer Hines (and a fantastic performance he does)
3rd Doctor - Tin Treloar
So there you go, that's my list. Any more anyone can think of? The rules are it has to be in a licensed production of a Doctor Who episode, it doesn't have to be canon, just licensed by the BBC and be an actual full Doctor Who story, not a skit or sketch within something else.