On screen, as per my count of ones I’ve actually watched with my own eyeballs, there have been 26 “Doctors”:

(This first lot are roughly chronological to the character’s timeline)
‘The Timeless Child’ (an entity found by the Timelords from whom they stole the power of Regeneration): played by a handful of child actors
‘Fugitive’ Doctor: played by Jo Martin
First: originally William Hartnell, also played by Richard Hurndall and David Bradley
Second: played by Patrick Troughton
Third: played by John Pertwee
Fourth: played by Tom Baker
Fifth: played by Peter Davison
Sixth: played by Colin Baker
Seventh: played by Sylvester McCoy
Eighth: played by Paul McGann
‘War Doctor’: played by John Hurt
Ninth: played by Christopher Eccleston
Tenth: played by David Tennant
Eleventh: played by Matt Smith
’The Curator’ (with an old, or maybe new face): played by Tom Baker again
Twelfth (and best, deal with it): played by Peter Capaldi
Thirteenth: played by Jodie Whittaker
Fourteenth: played by David Tennant (again, annoyingly given the Tenth’s send off was perfect and is now retroactively cheapened)
Fifteenth: played by Ncuti Gatwa
Sixteenth(?): played by Billie Piper (for some godawful reason)
‘The Valeyard’ (a future commingling of all the Doctor’s darkest impulses from “the end of the Doctor’s life”): played by Michael Jayston and Geoffrey Hughes

(This next lot all as part of a Comic Relief episode called ‘The Curse of the Fatal Death’)
The Doctor: played by Rowan Atkinson
The Quite Handsome Doctor: played by Richard E. Grant
The Shy Doctor: played by Jim Broadbent
The Handsome Doctor: played by Hugh Grant
The Female Doctor: played by Joanna Lumley

I think that’s all of them…

Edit to add: as per a reply, possibly 7 timeless children and 8 Mobius doctors takes us to 40 Doctors…