Selecting a single entry-point into the Doctor Who world is an often-debated topic on DW forums. Most suggest starting with a Tom Baker (not Colin Baker) episode, or even one of the current series with Matt Smith (I like his debut episode, "Eleventh Hour"). Tom is arguably the quintessential Doctor and his quirkiness is unlike any other character on screen. I like the Jon Pertwee episodes too because the stories are almost always good. You must be tolerant of low-grade special effects. Don't start with Sylvester McCoy (although a few of his episodes are very good too), and don't start with one of the movies.

If you want an idea of how incredibly clever the series can be, you could start with the David Tenant episode "Blink". That's my choice for a newbie intro, even though it doesn't follow the typical DW format. Tenant is my least favorite doctor, but that episode blew me away and is on almost everyone's short list of favorites.