In chronological order: Troughton; Baker, T; and Eccleston
I really can't make up my mind on the order of these three. Matt Smith comes a close fourth but I can't, with clear conscience, place him in the top three until I see more of him...
Interesting, considering Matt Smith has now been in as many episodes as Eccleston.
Only 18 for Troughton? I guess that's quite high given as to how few of his stories survive and how few nuWho viewers have never seen him.
But I do find it amazing as to how some people can just view two of his stories and instantly fall in love with his portrayal.
Besides -- Tom Baker, Colin Baker and Peter Davison can't be wrong since HE is their favorite Doctor. (In Tom's case, after him obviously)
I thought that Colin Baker's favorite was William Hartnell.
When pressed, I would probably single out Patrick Troughton as my #1 favorite. However, I'm very glad I got 2 extra votes for Tom Baker & Matt Smith. Tom Baker is always a reliable choice and Matt Smith is bringing nerdy back!
But honestly, there's just something about the brash confidence that Troughton's Doctor has, and yet he's not immortal. I think that he's the only Doctor that I can truly buy being put in mortal jeopardy. ("The Seeds of Death" is a great example.) It makes his confidence in the face of death all the more heroic.
Also, Troughton had such a great sense of comic timing. He was able to deliver the serious exposition seriously and yet he was always doing something to add an extra sparkle to the scene. He's a great actor that is always doing something that's interesting to watch and yet is never deliberately stealing focus. There are so many nice touches of this, particularly in "The Invasion." One of my favorites is in Part 2 where he & Jamie get cornered by the shadowy government guys, so he decides that there's nothing left to do but sit down on the curb and play cards as if nothing is happening.
It's truly criminal that so few of Troughton's stories survive intact. But one of the things that probably bolsters his reputation is his 3 multi-Doctor specials. In each one, he handily upstages all of the other Doctors there. (Although, it's a shame we never got to see him go toe-to-toe with Tom Baker. That would be a close match!)
Speaking of multi-Doctor specials, do you suppose there will ever be another multi-Doctor pairing that's as fun as Patrick Troughton & Jon Pertwee? Seeing those 2 bicker together was the best part of "The Three Doctors," "The Five Doctors," & even some of the random charity appearances where they appeared together.
A trout in the hand is worth two in the...erm...river.
Or Pond.
The great part about being a time traveler is that you can have one Trout in the Pond and one in the River at the same time. Lucky Doc!
My attempt at doing a ranking of all the Doctors:
1. Patrick Troughton, as I said before.
2. Tom Baker. When push comes to shove, I think he barely edges out Matt Smith. But then, lets see how it shakes out when Matt Smith finishes his 7th year.
3. Matt Smith. Bow ties & fezes are cool!
4. Paul McGann. Goddamn the 1996 movie not being available in the U.S.! I'm not sure his movie would have been the basis for a good TV show. But in the Big Finish audios, McGann conveys an authority like no other. He's dangerously powerful yet approachable at the same time. (I haven't listened to a lot of his audios, but I was especially impressed with his performances in "Scherzo" & "The Natural History of Fear.")
5. Christopher Eccleston. One of the more versatile actors, even though he was largely playing either angry or goofy. He still did it with a deft touch and often knew how to play as a counterpoint to the material.
6 & 7. Colin Baker & Sylvester McCoy. Both good, over-the-top actors that were frequently saddled with many of the show's worst scripts. But then, the 1980s were very unkind to an awful lot of people.
8. Jon Pertwee. He often feels less like the Doctor and more like an eccentric James Bond wannabe. Still, his charm is limitless.
9. David Tennant. When he started out, I ranked him at #1. He has since fallen way down on my list due to his incessant overacting. Whereas Eccleston was often able to show a certain amount of restraint, even during RTD's more melodramatic moments, Tennant's default setting was always to turn it up to 11.
10. Peter Davison. A good actor but a bit too bland to be the Doctor.
11. William Hartnell. He's kinda hard to judge against the others because it was such a different show back then. The appeal had less to do with the Doctor himself and more to do with the overall chemistry he had with Ian, Barbara, & Susan.