Introduction
Time travel
Space opera
Alien invasion
Forbidden knowledge
Fantasy
Genre benders and history twisters
Multiple-Doctor stories
Below are the main themes of Doctor Who, with the examples that I've reviewed.
Note: knowing the theme of a story may occasionally constitute a spoiler. You have been warned.
Same earth. Different point in time.

Into the past:
An unearthly child (1963)
Marco Polo (1964)
The Aztecs (1964)
The crusade (1965)
Father's day (2005)
Into the future:
The enemy of the world (1967 - 1968)
To boldly go where no man has gone before.

Reviews:
The Daleks (1963 - 1964)
The web planet (1965)
The tomb of the Cybermen (1967)
The space pirates (1969)
The ark in space (1975)
The Sontaran experiment (1975)
Genesis of the Daleks (1975)
The robots of death (1977)
The leisure hive (1980)
The keeper of Traken (1981)
Castrovalva (1982)
The caves of Androzani (1984)
Vengeance on Varos (1985)
Revelation of the Daleks (1985)
New Doctor Who:
The end of the world (2005)
They're here...

Reviews:
The Dalek invasion of earth (1964)
The Daleks' master plan (1965 - 1966)
The moonbase (1967)
The faceless ones (1967)
The evil of the Daleks (1967)
The abominable snowmen (1967)
The web of fear (1968)
The wheel in space (1968)
The invasion (1968)
The seeds of death (1969)
Spearhead from space (1970)
The claws of Axos (1971)
The hand of fear (1976)
Logopolis (1981)
The resurrection of the Daleks (1984)
Remembrance of the Daleks (1988)
The TV movie (1996)
Rose (2005)
Aliens of London / World war III (2005)
Dalek (2005)
The long game (2005)
Boom town (2005)
Bad wolf / The parting of the ways (2005)
Science and technology gone wrong.

Reviews:
Inferno (1970)
The green death (1973)
What if...

Reviews:
The edge of destruction (1964)
The celestial toymaker (1966)
The underwater menace (1967)
The mind robber (1968)
To me, these stories seem primarily idea-driven rather than plot-driven (though I realise this is a judgement call). Some appear to be one genre, but are actually something else; others provide alternative explanations for real historical events. The various writers who have worked on Doctor Who have come up with different versions of this general idea.

The Robert Holmes genre bender, a genre piece (usually a gothic horror tale) with a science-fiction story lurking underneath:
Carnival of monsters (1973)
Pyramids of Mars (1975)
The talons of Weng-Chiang (1977)
Horror of Fang Rock (1977)
Ghost light (1989)
The curse of Fenric (1989)
The unquiet dead (2005)
The empty child / The Doctor dances (2005)
The Douglas Adams genre bender and history twister, a heist story which turns out to be a science fiction story, which, in turn, provides an alternative explanation for the existence of life on earth:
City of death (1979)
The Eric Saward history twister. A science-fiction story that provides an alternative explanation for a historical event.
The visitation (1982)
Earthshock (1982)
The mark of the Rani (1985)
Fan fun.

Reviews:
The three Doctors (1972 - 1973)
The five Doctors (1983)
The two Doctors (1985)
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