Doctor Who is a fantastic show. Why? Because it contains great acting, great story writing, and fantastic humor. It's essentially a sci-fi show that takes place in modern times, but due to the ability of time/space travel it explores the "what ifs" of the future (and past).
Personally, I love it due to the extremely creative nature it has mixed with excellent humor in every episode. And to top it off, the show isn't simply a sit-com like format where episodes have no relation to each other. The writers actually tie in almost every single episode into a grand over-arching plot that develops not just over one season, but many seasons all together. The vision of the writers to look so far ahead in the show and plan it out so perfectly is amazing.
That said, I've only seen the "new" Doctor Who episodes (and some older movies), so I can only give a great recommendation on the newer series that started with Christopher Eccleston and afterwards.
As for watching it, Netflix has all but the most recent season. There are also plenty of websites that allow free viewing of them, but I've since lost the links to the good ones.