My girlfriend is a huge Doctor Who fan so she managed to get me interested pretty early on. We have undertaken the monstrous task of watching all of Doctor Who, and by all I do mean all. Right now we are in the third season of the William Hartnell episodes (the first doctor). It is pretty awesome stuff; early daleks always make me smile in that weird cheesy way.
The early episodes are a bit of a pain in some ways though. A lot of them are audio only because the film stock holding the visuals is lost entirely, meaning scenes had to be either reconstructed from other footage, or pictures had to be used to help convey the story with captions describing what is happening on screen. It requires dedication to sit through some of these, that's for sure, but the payoff's worth it.