36. The Tenth Planet (First Doctor)
This story comes close to being ineligible because one of the four episodes are missing, but it still qualifies. The Tenth Planet is the final appearance of the First Doctor (until The Three Doctors, see #40), and the first episode to feature the regeneration sequence. The story follows a strange planet somehow approaching Earth, and the Doctor reveals it to be Mondas, the tenth planet in our solar system. Mondas was once a sister planet to Earth, but the inhabitants slowly retrofitted their bodies with mechanical parts until all that remained was the brain. They called themselves Cybermen. In addition to this being the introduction to the Doctor's regeneration, it also introduces the Cybermen, albeit looking very different than many of us are used to.
35. The Sea Devils (Third Doctor)
This six-part story follows the third Doctor and his companion Jo Grant as they visit The Master in an Earth prison run by UNIT. While there, they learn of the mysterious disappearances numerous ships nearby. It turns out these ships vanishing are due to the actions of The Sea Devils, an underwater race similar to the Silurians (never heard of them? Stay tuned, we'll get to them around #28).