John Pertwee. Many of the episodes were very well written and others were somewhat over the top, but Pertwee played the Doctor with such a fervent seriousness about him that he managed to maintain a certain dignity even in the midst of the most ridiculous backdrops. Dr. Who was an alien with extreme intelligence and Mr. Pertwee could not only spit out the heady sounding verbiage but do it in a manner that showed his constant frustration with the stupidity and bureaucracies of man, and do it with characteristic British wit. This was always a delight to watch. Of course, the Brits have a long tradition, beginning with Arthur Conan Doyle, of portraying the genius detective trying to solve a puzzle, or an alien mastermind trying to save the planet in this case. Dr. Who could almost be described as the Sherlock Holmes of science fiction.
I should also mention that I always loved the theme song. The original recording was an early example of heavy synthesizer composing. There was something mesmerizing about it, especially when you add in the visual which would today be described as one of those weird media player mixer skins. Here is a sample of the starting theme from the Pertwee era - Dr. Who Title Sequence. There's also a nice major key interlude in the full recording if you can find it in the U.S.
A few decades later, my first venture into the newly popularized world wide web was via the old hosting platform called Compuserve. This was kind of like an AOL for computer people that focused on professional resources, but it also had chat rooms of every sort which I spent a good deal of time in until the novelty wore off. In one of these, I met a lady in the Midwest who happened to be an avid Dr. Who fan. When she found out I actually knew who that was we began talking about the subject and I made the shocking discovery that there had been 7 different people who had played Dr. Who over the entire initial run (and some others in attempts to resurrect the series much later). John Pertwee was Doctor #3. My friend said her favorite was Doctor #4, played by Tom Baker. She had a whole video tape library of past episodes and she was so happy to be able to chat about the topic that she sent me a whole set of video taped episodes featuring several of the different Doctor's. Included were two episodes that had all the doctors appear together in some type of time warp story (the 3 doctors and the 5 doctors). The idea was that the Doctor changed his appearance from time to time via "regeneration" if he was injured in order to maintain his long life span. This made it easy to allow him to go back in time and meet himself without having to do any special effects. Watching my friend's tapes allowed me to bring back the memories and also add to them the new knowledge of the series.
After seeing some of the earlier and later episodes, I still consider John Pertwee to be the best. I may be biased, but the whole series takes on a different personality for each Doctor, including the production, directing, and script writing. For example, only Pertwee's doctor is banished to earth and works closely with a military operation called U.N.I.T., so most of the stories take place on earth and take on sort of a government operative feel to them. None of the other Doctors were as serious in manner as Pertwee, and he has some great stylistic additions like his black cloaks and vintage jalopy that he liked to drive around. I can understand the appeal of Tom Baker, who was supposed to be one of the most popular and the longest running. He gets some pretty good scripts (I've just found out some were written by the Douglas Adams), but also adds a more light-hearted approach. He even owns a robotic dog named K-9 that follows him around. But for my taste, I'll take the serious scientist over the eccentric wanderer.