(or "The Perfect Engine")
Disclaimer time, here: I'm a bit biased when it comes to Doctor Who. I've been watching the series since I was two years old, I have loads of Doctor Who DVDs and videos, and I currently type this in a room with bookshelves stacked from top to bottom with Doctor Who novels, Doctor Who trade paperbacks, Doctor Who audio plays, and non-fiction books about Doctor Who.
On the other hand, a) that does make me pretty well-informed on the series, in all its various incarnations, and b) that's a lot of incarnations of Doctor Who. Doctor Who is one of those rare concepts that has been adapted to every medium; there have been Doctor Who stage plays, Doctor Who poems, Doctor Who movies and radio plays and comics and yes, a television show that still holds the record as the longest-running science-fiction series in television history. So what is it that makes the concept of Doctor Who as enduring as Superman, Batman, and Sherlock Holmes?
The key, I think, is to look at the elements that have persisted throughout its forty-five year history. Because actors have come and gone, characters and settings have changed, and the show has constantly renewed itself over the years ("regenerated", one might say.) But the constant? It's about a mysterious man with a magic box that can go anywhere in time and space.
That's a concept that doesn't need any help at all to generate ideas. The supporting cast can change, the antagonists can come and go, but any writer who can't do something with "anywhere in time and space" doesn't have any business being a writer. Every other book, every other storytelling engine can be ground up and fed into Doctor Who's mill. The Doctor can wander through any historical adventure, he can bump into any science fiction trope, and because of that, there's no end to the number of potential adventures he might have. The only limitation on the series becomes the length of time an actor is willing to put into the part, and a stroke of genius early on even solved that problem.
Even the Doctor's enemies are endlessly reusable. Pitting him against monsters instead of villains allows writers to bring back even the most definitively-killed enemies for another go-round; when you fight entire species of bad guys, nothing short of an extinction-level event is going to stop you from coming back to challenge the Doctor again and again. (And as the Daleks have proven, even those aren't necessarily a barrier. Time machine, remember?)
The strength of Doctor Who is that its concept is so simple and elegant that it can be adapted to fit any other parts that come to mind. It's like a Universal Adaptor for stories, constantly renewing itself by learning from the things around it. One day it's Hammer Horror, the next it's Buffy with time travel. In a hundred years' time, when so many series have been forgotten, I fully expect to see the Thirtieth Doctor and his companions fighting the Daleks on some alien planet. And I look forward to every story between now and then.