Here's my recommendations:
FIRST DOCTOR
The Aztecs-A good 'historical' story that has no sci-fi trappings apart from the Doctor and co himself. A companion gets mistaken for an Aztec goddess and there is a moral quandry about changing time.
The Time Meddler-The Doctor first encounters another time lord in 1066. Lots of fun.
The Romans-Doctor Who does the historical again, but this time with a comic touch.
SECOND DOCTOR
Not much exists of the second Doctor, unfortunately, but check out TOMB OF THE CYBERMEN (A fun, if low-budget looking story) and THE WAR GAMES (Which introduced the time lords proper, gave an origin story for the Doctor, and is an epic story in it's own right). The Mind Robber, similar in some ways to Star Trek TOS's Shore Leave, is also good fun.
THIRD DOCTOR
SPEARHEAD FROM SPACE-The only classic series story shot entirely on film (and the very first in color), this is the first appearence of the Autons/Nestenes, The Third Doctor, and is overall a good introduction to UNIT in the classic series (Although they appear first in THE INVASION).
INFERNO-Doctor Who does the Mirror, Mirror concept when the Doctor accidentally winds up in an alternate universe.
THE DAEMONS-Probably the best of the stories featuring the original Master, Roger Delgado. The Master basically summons an alien 'devil' and the Doctor and UNIT must deal with it.
THE GREEN DEATH-A literally 'green' Doctor Who where the Doctor must stop a corporation from pollution that creates nasty mutant maggots which turn into cheap-looking flys

.
THE TIME WARRIOR-The first appearence of Sarah Jane Smith and the Sontarans, also one of the better-looking stories production wise.
FOURTH DOCTOR
Genesis of the Daleks-The origin story of the Daleks, and the first appearence of their creator, Davros. The Doctor also confronts several moral dillemas in this episode.
Pyramid Of Mars-The Doctor battles an alien that inspired the ancient Egyptians. A creepy gothic story.
City of Death-A fun romp through Paris as the Doctor and fellow time lord/lady Romana try to stop an alien from erasing human existence.
FIFTH DOCTOR
Kinda-A sort of metaphysical WHO where the Doctor confronts a nasty monster who possess people and that physically manifests itself as a huge fake looking snake
Earthshock-The Cybermen return in force in this story, which sees the tragic fate of a companion.
Mawdryn Undead-Sort of the 'relics' of Doctor Who as the Doctor meets his old friend Brigidiar Lethbridge Stewart who is now retired and amnesiac.
Caves of Androzani-One of the best DW stories, this story is pretty much the core of what the Doctor is all about.
SIXTH DOCTOR
Vengeance on Varos-The Doctor finds himself in a nightmarish dome of horrors as several people watch him on TV.
Revelation of the Daleks-An oddball but well-directed Dalek story.
SEVENTH DOCTOR
Rememberance of the Daleks-The Doctor returns to London in 1963 where it all started in a deadly gambit with two Dalek factions.
Ghost Light-A fun if confusing story partially about creation vs. Evolution.
Curse of Fenric-The Doctor plays a deadly game of chess with an entity as old as time itself in the midst of World War II. Plus we learn a lot of a companion's backstory, and the climax is quite shocking.