On television there are the main 12 (Wiiliam Hartnell, Patrick Troughton, Jon Pertwee, Tom Baker, Peter Davison, Colin Baker, Sylvester Mccoy, Paul Mcgann, Christopher Eccleston, David Tennant, Matt Smith, and Peter Capaldi).
John Hurt appeared in "The Name of the Doctor" as an incarnation of the same Time Lord(but one who does not call himself 'the Doctor').
Michael Jayston and Geoffrey Hughes both portrayed The Valeyard, a possible future version(said to exist 'between the Doctor's twelfth and final incarnations').
Toby Jones played The Dream Lord, made up of aspects of the Doctor.
Richard Hurndall played the First Doctor in "The Five Doctors", replacing the deceased William Hartnell.
Adrian Gibbs played The Watcher in "Logopolis", the avatar of the future Doctor.
Various actors were body doubles, stand-ins, stuntmen etc. As just two examples, Edmund Warwick was the First Doctor for some shot-from-behind shots, and Terry Walsh appeared as the Fourth Doctor for some of the fight scenes in "The Sontaran Experiment".
Eight different members of the Production Team were supposed to be identified as pre-William Hartnell Doctors in "The Brain of Morbius", though this is now hotly debated.
In other media:
Peter Cushing played "Doctor Who" in the 60's Dalek movies(and a pilot for a radio spin-off).
Rowam Atkinson, Richard E.Grant, Jim Broadbent, Hugh Grant and Joanna Lumley played the 9th through 13th Doctors in "The Curse of Fatal Death".
Richard E. Grant also played the original canonical Ninth Doctor in "Scream of the Shalka"(a totally different incarnation to his appearance in COFD).
Trevor Martin("Seven Keys To "Doomsday") and David Banks have both played (different) Doctors in stage plays.
Nicholas Briggs, Arabella Weir, David Warner, David Collings, Ian Brooker, and Geoffrey Bayldon have all played different versions of the Doctor, all deliberately set in alternate realities in big Finish's "Unbound" Audio series.
There have also been various unofficial(ie. Unlicensed actors playing the Doctor), most famously Nicholas Briggs in The Audio Visuals.
And there have been various actors playing characters thought to be the Doctor, eg. David Morriseey as Jackson Lake in "The Next Doctor".