Okay, after digging a little more into Classic Who - where the special effects take some getting used to, but most of the stories are pretty great - I now know:
The Caves of Androzani
Earthshock
City of the Dead
The Talons of Weng-Chiang
Logopolis
The Web of Fear
(plus the existing footage of The Evil of the Daleks and The Celestial Toymaker, but that doesn't really count)
The Enemy of the World is on my list to check out soon, as is The Deadly Assassin, as I've heard there's a lot of Gallifrey in that one, but since there's so much to watch, it's quite daunting. Does anyone have any recommendations for any stories that are must-watches, that I should check out post-haste?