The first time I encountered Doctor Who I turned it off. YTV was running Doctor Who just before Teenage Mutant Ninja Turtles (TMNT). Our TV at home didn't go above channel 13 and YTV was channel 22, so I had to go over to my Grandparents house around 5 to watch it.
My opinion of Doctor Who changed. Later in the year I began watching the ends of the episodes and at some point must have been pulled in by one of the cliffhangers. I don't remember the story that I became a regular viewer. I remember watching a lot of the Seventh Doctor's stories (all of them) and most of the Sixth's -- especially A Trial of a Timelord. My dislike of the Sixth Doctor I recall focused on how mean he was to Peri (one of his companions). I also remember watching a lot of the First, Third and the first few stories of the Fourth Doctor.
The next year I was in England for my step-father's sabbatical year. Though Doctor Who was not running there (it had wrapped up a year or two earlier), the local branch of the library had many of the novelizations of the the long-running series. The Central Library had even more. I read all of the novelizations that I could get my hands on -- from First Doctor stories like the two-volume Dalek Master Plan to Fourth Doctor stories like Image of the Fendahl and The Face of Evil.
After devouring the novelizations and getting my first Doctor Who reference books, I returned to Canada where I continued to watch the series (and learned what this Red Dwarf thing was that my classmates had been watching when Sherlock Holmes was on). Soon after the New Adventures novels began release. One of my uncles gave me the first one or two of these. They followed the Seventh Doctor and Ace on their continuing adventures after Survival, the last aired story. It wasn't until years later that I found out about Andrew Cartmell's "master plan" in his depiction of the Doctor. However, even not knowing it, I loved it. I read everything I could get my hands on, and was rewarded with the release of the Handbook series covering each Doctor.
A lot of time has passed since then. Doctor Who has gone from being cancelled, to being reintroduced as a made-for-TV movie (that was ultimately disappointing for a purest like me), to being relaunched even more years later in its current incarnation which has been running six seasons now. I still like watching episodes of the classic series, still haven't caught up on all of the Fourth and Fifth Doctor stories, but I'm not worried. I'll have plenty of new Who to watch in the upcoming years and the off-seasons to catch up on the classic series.