Here is a great list of all of the classic Doctor Who DVDs that Netflix has in their proper chronological order. Below I’ll list just the ones that you can watch instantly as of today. No guarantee they won’t add more or remove these in the future, of course.
- The Aztecs
- The Mind Robber
- Spearhead from Space
- The Three Doctors
- Carnival of Monsters
- The Green Death
- The Ark in Space
- Pyramids of Mars
- Horror of Fang Rock
- The Ribos Operation
- The Pirate Planet
- The Androids of Tara
- The Power of Kroll
- The City of Death
- The Leisure Hive
- The Visitation
- The Caves of Androzani
- The Curse of Fenric
I don’t know why the DVDs that are available to stream were chosen and not others. Many of the ones I understand to be the essential stories are DVD-only. Of those that can be streamed, all but the Sixth and Eighth Doctors are represented (though Eight only appeared once, anyway).
It should be said that Doctor Who is not a terribly continuity-driven show. There’s no need at all to start at the beginning. The series since 2005 stands alone very nicely, and I certainly recommend starting with the newer series first before going back to watch the older episodes. Season five (the most recent) is a great jumping-on point if you don’t want to go back to season one (though you should!). Here are the newer seasons on Netflix:
- Season One
- Season Two
- Season Three
- Season Four
- The Next Doctor
- Planet of the Dead
- Waters of Mars
- The End of Time
- Season Five
Season five isn’t streaming yet, but it just came out on DVD so there might be a waiting period. There was an almost two-year break between seasons four and five, so the four special episodes (The Next Doctor through The End of Time) fill that gap and are crucial to the development of the Tenth Doctor’s character.