I would probably say Troughton. While Hartnell originates the character, it seems to be Troughton that defines how the later Doctors do things. It might be that the writers decides that this was how th Doctor was, or maybe it was that the later actors who played the Doctor were inspired more by Troughton than Hartnell. The main one that is different is of course Tom Baker, who from what I can tell, was being Tom Baker. The writers were still were probably still doing the Doctor (as based on Troughton), but Baker does what he does. And it wonderfully sticks to the Doctor until the present. Today, the writers write a script for the Doctor. Then you get an actor who plays the Doctor. At that point the personality of the new actor changes the way it works in little ways so it becomes them as the Doctor. The basic Doctor doesn't change. Throw 1960s Patrick Troughton into a modern episode of Doctor Who and while you'd get a different preformance, you would still get The Doctor. You put William Hartnell in there and I'm not sure what you'd get. Probably the Doctor, maybe.
Character wise, Hartnell's Doctor is pretty much the core of all the Doctors exposed raw, giving us a good view of his positive AND negative traits (none of which have really gone away, just diminished). Other than that though, probably Tom Baker's Doctor. He was the one who sold the Doctor as being a over the top eccentric... When in reality only Tennant and Smith's Doctor's have been anywhere near as eccentric.
There seem to be two general patterns for the Doctor 1) Paternalistic/Crusty: Hartnell, Pertwee, Colin Baker, Capaldi 2) Quirky/affable: Troughton, Tom Baker, Davison, McCoy, McGann, Tennant, Smith Not sure where Eccleston falls. More followed Troughton's general approach so I'm going with Troughton. Mr Awe
Ithekro and Mr. Awe sort of beat me too it. All subsequent Doctors seemed to be some combination of Hartnell, Troughton and Pertwee - Tom Baker - goofy but competent (Troughton) with a dash of vigor (Pertwee) Davidson - vigorous (Pertwee), selfless (Troughton) often short-tempered (Hartnell) Collin Baker - Arrogent and opinionated (Hartnell), goofy appearance (Troughton) McCoy - Goofy on the outside (Troughton), bit mysterious and manipulator (Hartnell) McGann - Dressed like Pertwee had a heart like Troughton Eccleston - A Doc of action (Pertwee), definate distant, darker side (Hartnell - especially in Edge of Destruction) Tennent - Energetic and pompus (Pertwee), humor and compassion (Troughton) Smith - Troughton all the way, with a bit of Pertwee thrown in Capaldi - Hartnell's demenor with Pertwee's wardrobe and pomp Like Kirk, Spock and McCoy, you have action (Pertwee), Mind (Hartnell) and Heart (Troughton). Given the choice personally - Troughton.
For me they are all the Doctor, because they all bring something to the role, like lamps shining at different angles on the same statue. I think the great loss is McGann, someone will have to explain to me why RTD didn't go with him, there was no reason not to, or why Moff didn't have him instead of the War Doctor (great as Hurt was), again, no reason I could see. But I appreciate them all. They are all the Doctor.
Now the other way to see this question would be: "Which actor who played the Doctor is the Doctor?" To that question the answer is, "Tom Baker". If there was anyone who you could point to and say, "That's the Doctor" it is Tom Baker. Patrick Troughton's Second Doctor is pretty much the definative Doctor as almost all of them seem to have a piece of that Doctor in them, more so than any other, even Hartnell's Doctor at times. But if you had to say which actor is the Doctor, it is Tom Baker.
See, I think Hartnell gets unfairly pigeonholed as crusty or grumpy based on his early episodes, but by the time you get to the Vicki era (The Rescue/The Romans) he's downright genial and even giddy. There's no aspect of the later Doctors that isn't somehow present in Hartnell's Doctor. But, that said, I agree that Troughton added an emphasis that the later ones mostly incorporated, which was a tendency to play the fool like Columbo to get information and not let on how far ahead of people he was. Hartnell's Doctor did that occasionally, but didn't make a habit of it.
McGann did shine. It's wonderful to see how he nailed the role of the Doctor so perfectly, so fast - and then did it all over again after 17 years. Maybe there's some other universe in which the show was revived and he did a 3 or 5-year run... There was an interview Tom Baker did while he was playing the Doctor, in which he stated that he made an effort to make sure his public behavior was in keeping with what people expected of the Doctor. In other words, he never wanted a situation to happen where the fans - especially little kids - would see 'Doctor Who' behaving badly (ie. being obnoxiously drunk in public, or causing some other kind of disturbance). He was very aware that some fans don't separate the actor from the role, so he took care to keep his private life private.
I like Hartnell the best, but Tom Baker and Dave Tennant are the iconic ones. Matt Smith was lucky enough to be the Doctor when the show truely cracked the American mainstream market, though, so I wouldn't be surprised if there's a fanbase there that strongly identifies him as 'The' definitive article over Tennant. In the UK and Australia though I think it would definitely be T. Baker and Tennant.
Matt Smith all the way. On the few occasions when it was required, his age and the weight of all those centuries felt real in a way that no other actor has been able to pull off, IMHO. Ecclestone is a close second.