The most recent era of Doctor Who has been full of time warps. The show about an alien in a time machine has been delving into the weird ramifications of time travel more than ever before, including the Doctor's time-crossed relationship with River Song.
But the show about a mysterious transdimensional blue box has always included storylines about time travel. At least once or twice a year, the show did a story in which the time machine actually influenced the plot, instead of just delivering the Doctor and his friends to a new adventure. Here are all the old-school Doctor Who stories that actually deal with time travel as a plot device.
Top image via PunkAyame36, artist unknown.
First, let's explain our criteria — most Doctor Who stories include the TARDIS, his magical time machine. But just as many Star Trek episodes feature the Enterprise delivering Captain Kirk to a new planet where the action takes place, most classic Doctor Who stories involve the TARDIS showing up someplace and then being left behind (or lost) until the adventure is over.
So here are the classic Who stories where time travel is actually what drives the story:
An Unearthly Child (1963). The show's first serial also includes the first time the TARDIS travels through time, depositing the Doctor, his granddaughter Susan and two schoolteachers in a prehistoric era full of weirdly Shakespearean cave people. This is the only time the TARDIS makes a trip in the middle of a serial until 1965. (See below.)
The Edge of Destruction (1964). Mostly, this is a "bottle" episode in which our heroes are trapped inside the TARDIS and strange things are going on — but the actual peril is that the TARDIS will travel back to the beginning of time and be destroyed.
The Aztecs (1964). The early years of Doctor Who featured a number of "historical" stories in which the TARDIS crew shows up in some famous era, gets caught up in events, and then escapes. But "The Aztecs" is unique in that the Doctor's companion, Barbara, actually wants to change history, and the ethics (and plausibility) of doing so are debated quite a bit.
The Space Museum (1965). Due to a weird TARDIS malfunction, the crew jumps ahead on their own time track and sees a future in which they've all been turned into immobile exhibits in a museum, trapped apparently forever. Then time winds backwards, and the crew has a chance to change their own future.
The Chase (1965). The Daleks decide to get rid of the Doctor once and for all — so they build their own time machine and chase the Doctor through time and space. That's about it. This storyline is repeated somewhat in the following season's "Daleks' Master Plan," although there the pursuit is mostly through space, with a bit of time mixed in. (That latter story also features a weapon which ages people to death.)
The Time Meddler (1965). The third of three time-travel stories in a row, this one features a member of the Doctor's own race who is trying to do what Barbara failed to — rewrite history. He wants to arm the Anglo-Saxons with advanced weaponry so they can prevent the Norman conquest in 1066. Just because.
The Ark (1966). This is an unusual story — because the TARDIS travels forward in time halfway through. The survivors of humanity are aboard a giant ark taking them to a new home planet, and the Doctor helps them deal with an outbreak of the common cold, to which they've lost immunity. But when the TARDIS jumps forward 700 years, the humans' servants, the Monoids, have enslaved humanity.
The Evil of the Daleks (1967). A Victorian inventor is trying to create a time machine using mirrors and stuff — but what he gets instead is a visit from a group of homicidal cyborgs who want to set a trap for the Doctor. There's a lot of shuttling back and forth between Victorian England and the 1960s, followed by a trip to the Dalek homeworld in (probably) the far future.
The War Games (1969). People are being kidnapped from famous wars throughout human history. (Well, European and North American history, really.) And they're fighting in a giant conglomeration of fake wars on another planet, so that their time-traveling masters can create the most unstoppable army out of those lucky enough to survive. This plan makes no sense, unless you just go with it. Anyway, the Doctor has to enlist the aid of his own race to get all the time-kidnapped soldiers home.
The Claws of Axos (1971). The giant space parasite, Axos, is obsessed with learning the secret of time travel — and even though they've got their own captive Time Lord, the Master, they still want the Doctor's help. Not surprisingly, the Doctor outwits them. I believe this is the story that introduces the idea of the "time loop," in which someone is stuck looping endlessly through time.
Day of the Daleks (1972). Arguably the first Doctor Who story to feature an actual time paradox, this story involves freedom fighters from the 22nd century going back in time to prevent a Dalek takeover of Earth — only to discover that they're trapped in a kind of causal loop, which is different from the one the Doctor trapped the Axons in.
The Time Monster (1972). This is the story which shows most clearly the perils of focusing too much on the show's own mythos — there are some fascinating ideas here about time travel, including what would happen if two TARDISes tried to occupy the same space, and lots of crazy time shenanigans. But as a story, it's kind of a bloated mess. The Master impersonates a college professor so he can build a time machine called TOM-TIT (even though he already has a much better time machine) so he can enslave a time-eater from Atlantis.
The Three Doctors (1973). The Doctor meets two of his past selves, and remarkably little in the way of the paradoxical happens.
Carnival of Monsters (1973). Someone has kidnapped creatures from all over time and space, including a boatload of 20th century humans, and placed them inside a rather shabby fairground attraction, where they're miniaturized and kept in an endless time loop. Until the Doctor shows up and ruins the whole thing.
The Time Warrior (1973-1974). Like Barbara and the Meddling Monk before him, a Sontaran warrior is attempting to change history — this time, just so that he can get a place to crash while he repairs his spaceship and goes home. Rather unusually, this time around changing history is just a random byproduct as far as the villain is concerned.
Invasion of the Dinosaurs (1974). The dinosaurs don't actually invade — you sort of picture them all wearing military uniforms and being led by a dinosaur general and stuff. Instead, some mad scientists are bringing dinosaurs forward in time from the prehistoric era, so they can empty London to give them breathing space to work on a plot to bring a bunch of humans back in time to prehistoric times to start humanity over, Terra Nova-style. (Why didn't they just work on their plan without bringing a bunch of dinosaurs forward in time?)
Genesis of the Daleks (1975). This one is rather unusual, in that the Doctor himself is sent back in time to change history — to do what Barbara, the Meddling Monk, and a random Sontaran all failed to do. He's on a mission to prevent the creation of the Daleks, or else to deal them an early setback or learn about some basic weakness in their design. Spoiler alert: He more or less fails.
Pyramids of Mars (1975). This one is debatable — the evil Sutekh builds a time tunnel, but pretty much only uses it to travel through space, until the Doctor screws around with it.
The Masque of Mandragora (1976). The Mandragora Helix hijacks the TARDIS and takes it to Renaissance Italy, where it plans to — what else? — change history, by killing or controlling a bunch of Renaissance geniuses.
The Talons of Weng Chiang (1977). Weng Chiang isn't actually a fake Chinese god that no real Chinese person has ever heard of — rather, he's a criminal from the 51st Century (yes, the same era as Captain Jack and River Song come from). He's seeking to repair his rather lackluster time machine so he can return home, even though the first trip melted his face somewhat.
The Armageddon Factor (1979). Mostly notable because the Doctor uses our old friend, the Time Loop, to keep a dangerous situation under control while he figures out a solution.
City of Death (1979). Scaroth of the Jaggeroth explodes his spaceship on a primeval Earth — and as a result, he's broken into a number of separate selves, scattered throughout time. The telepathically linked splinters of Scaroth work to build a time machine so they can go back and stop the ship exploding, not realizing (or caring) that this will prevent humanity from ever evolving.
Meglos (1980). Mostly notable because this time around it's the Doctor being put into a Time Loop — which is renamed a Chronic Hysteresis, and can be defeated by play-acting.
Warriors' Gate (1981). At the meeting place between universes, there's a weird old castle where the past and the present collide, and you can find yourself slipping between the two timelines without any warning. One of the weirdest and most confusing classic Who stories, this one is not for the faint of heart.
Castrovalva (1982). When the Master comes back, so do a lot of his old tricks — including the TARDIS-inside-a-TARDIS trick, in "Logopolis." And in this story, we see the return of the "flying the TARDIS back to the beginning of time" trick first seen in "Edge of Destruction." Also, the Master apparently uses time travel to set up the fake land of Castrovalva, so it'll seem a convincingly old place and the Doctor will become trapped there.
The Visitation (1982). Notable for the suggestion that the Doctor actually causes historical events to happen, in this case the Great Fire of London. Also, in "Earthshock," the Doctor apparently helps cause the extinction of the dinosaurs.
Time-Flight (1982). I don't really know what in creation this story was about — but it does involve an airplane being stolen from the early 1980s and whisked back to a prehistoric era without any dinosaurs or other creatures. For reasons that remain unclear, to this day.
Mawdryn Undead (1983). In this story, we find out what happens if you meet your own past/future self — a nasty explosion, a case of amnesia, a spot of PTSD, and a closed loop in which your future self is doomed to meet your past self, pretty much no matter what. This has been ignored rather a lot in recent stories, however — and given that this story contradicts the history of the Doctor's friend, the Brigadier, it's possible the whole thing takes place in a pocket reality that collapses immediately afterwards.
The Five Doctors (1983). Mostly notable because we find out where the baddies in "The War Games" got the idea of kidnapping fighters from all across time and forcing them to fight — from the Time Lords themselves, who were doing it for a long time. Plus, another instance of the Doctor meeting his past selves.
The Awakening (1984). Another story in which I'm not sure what happened — but the 17th century and the 20th century are colliding and people are bleeding from one to the other. It's all because a church gargoyle is trying to make the English Civil War happen again, so he can belch smoke at everyone.
Resurrection of the Daleks (1984). Mostly notable because the Daleks build a time tunnel for reasons that remain unclear. They want to hide some samples of a deadly Dalek-killing disease someplace, so they build a time tunnel from a far-future spaceship to 20th century London, where absolutely nobody is guaranteed to snoop around.
Attack of the Cybermen (1985). This time, the Cybermen want to change history — this time smashing Halley's Comet into the Earth in 1985, so that they can avert the destruction of their homeworld in 1986.
The Two Doctors (1985). The Doctor meets a past self for the third and final time in the classic series — and this time around, we see that anything that happens to the earlier Doctor has a delayed but pronounced effect on the later Doctor. When the Second Doctor turns into an Androgum, the Sixth Doctor slowly starts changing as well. Also, when the Second Doctor gets shot by Sontarans, the Sixth Doctor seems to feel it across the centuries.
Timelash (1985). Thanks to Bluehinter for reminding me of this one. The eponymous "timelash" winds up sending an alien princess from another world to 19th Century Earth, where she (and the Doctor) meet H.G. Wells.
Trial of a Time Lord (1986). Thanks to Hypnosifl for reminding me of this one. The Doctor meets Mel for the first time, but she's actually met him before because she's from his future. Also, the Doctor gets to see an adventure he hasn't gone on yet. And the Valeyard is theoretically a possible future version of the Doctor.
Time and the Rani (1987). The Rani wants to build a Time Manipulator, which will allow her to control time. This is worth wearing a ridiculous wig for — although not as ridiculous as the wig the Doctor briefly sports.
Dragonfire (1987). A "time storm" takes Ace from 1980s England to the far future on Iceworld. This is later revealed to be the work of the evil Fenric.
Battlefield (1988). Thanks also to Bluehinter for the reminder about this one — the Doctor meets a group of Arthurian characters who know him, because they've already met a future Doctor. The future Doctor even leaves notes for his past self.
Silver Nemesis (1988). Lady Peinforte uses magic (apparently) to travel from the 17th century to the 20th.
The Curse of Fenric (1989). As various commenters have pointed out, this not only explains Ace's "time storm," it also features Ace meeting her own mother as a baby. And Fenric brings a haemovore back in time from a polluted future that the haemovore actually helps to cause, thus creating another stable time loop.
Did we miss anything?