Several early Doctor Who episodes are missing. Why? The prevaling theory is that the tapes on which they were recorded were overwritten by other BBC programs. In 1963, TV shows were recorded on "kinescope tapes" which looked like the big tapes on a reel-to-reel recorder or an old-time computer tape drive. They were expensive, they had a miniscule recording space by today's standards, and they took up a lot of storage space, so the BBC, in it's infinite wisdom, decided to reuse tapes that they would obviously never need again. Oops, how about a weekly children's show featuring weird monsters, a testy old guy, and an obviously impossible machine that seemed to think for itself? As time went by (Did Dr Who ever say that?) the BBC realized that they might have a hit on their hands and made sure that the later episodes were saved, so most of the damage was done to the William Hartnell and Patrick Troughton series.
I originally thought that there must be another problem with missing episodes since some stories with, say 4 episodes aren't entirely missing, they're just missing some episodes, maybe 2 and 4. The longest Dr Who story, the 12 part "The Dalek's Master Plan" is missing episodes 1, 3-4, 6-9, and 11-12. That wouldn't compute if it was possible to put 4 episodes on a single kinescope tape as we can now with DVDs but it would make sense if only one episode would fit on a kinescope tape. Still, missing some episodes of a story is more annoying than missing the whole thing. It looks like someone just grabbed a tape at random when they needed one.
Some Dr Who kinescopes have turned up in TV station archives in other countries, one in Hong Kong, and another in New Zealand, so if you work for a TV station, take a look through their old kinescopes and see if any of them have Dr Who written on the label.
If you find one, call me!