Awesome links guys! I wasn't actually aware of all those different versions.
Delia Derbyshire is the main person of interest to me - I'm rusty on the history but I believe the early versions of the theme weren't done on "synthesizers" as we think of them - it was more primal electronic music more like a mad scientist's laboratory like in the picture chromium posted - also musique concrète, using "non-musical" sources, bent into musical shape.
I think I was fortunate to discover Dr. Who at an early age - even though I had seen Star Wars by then, when I was watching Dr. Who I could totally buy into the stories, even the effects. I remember watching the "The Ark in Space" and the worm-creature that crawls along the corridor was creepy and gross! Watching it many years later on DVD it is painfully obvious that it is someone wrapped up in green bubble-wrap! I guess that was an advantage of just having a small black-and-white TV!
Even though the original episodes may not hold up now, they do provide background for the current episodes - finally finished watching the 50th anniversary episode and I thought it was great!