Dr Who - changes
When the original series was first broadcast, it was an almost instant success. Almost, but not quite, because it did not achieve high viewing figures until the Doctor's arch enemy, the Daleks, were introduced. This signalled a change in focus, away from the educational towards a kind of 'monster of the week' approach.
Flexible
This gives us an immediate clue as to why the series was popular; it gave people what they wanted. The format was flexible enough to accommodate this kind of response to popularity. The Daleks were going down well, so they were brought back, and then there were all the other monsters aspiring to be the next Daleks. The purely historical series without any science fiction features were eventually dropped.
Which doctor?
The series could sustain itself in spite of other kinds of changes too: the Doctor gradually said goodbye to his original companions and acquired new ones. Then after three successful years an even more drastic changed was carried through: William Hartnell, who played the Doctor, was replaced by Patrick Troughton.
This was not simply a matter of a different person playing the same part; the Doctor was supposedly able to change his physical appearance and personality. But Troughton played the Doctor with a very different character. Hartnell's rather severe old man was replaced by a gentle clown-like man who appeared to be much younger. Once this change was successful, the series had the potential to run indefinitely, as long as it could be injected with new ideas.
Writers
However even before this very visible change, there had been other changes behind the scenes: the series was the brainchild of Sidney Newman and Donald Wilson, who had senior positions at the BBC. They handed it over to producer Verity Lambert and script editor David Whitaker.
Before the first change of lead actor both of these had been replaced, and (as is common in TV) different writers wrote different adventures. As a result, the series never really belonged to any one person, and never tried to reflect a single person's vision or ideas.
The people who wrote it were first and foremost writers for TV and only secondarily writers of science fiction; often they had successfully written other kinds of scripts, perhaps police drama or comedy. If this meant that the science was sometimes inaccurate, it also meant that the writers knew how to entertain, to hook an audience, and to respond to audience demands.
Dave Ferguson, July 2006



