Stable Time Loop / Doctor Who

Several of these feature in the core TV series;

• In the First Doctor serial "The Myth Makers", the Doctor knows of the Trojan Horse from history, and at first dismisses it as an absurd literary device; then, after he rejects his first idea to breach Troy's walls, he invents the Horse himself, so it becomes history.
• In the Third Doctor serial "Day of the Daleks", humans from the future attempt to blow up UNIT headquarters to prevent someone from bombing a ministerial-level conference to be held there, starting World War III and allowing the Daleks to invade. As it turns out, it is their bomb that they are trying to prevent.
• There's also "City of Death", in which an alien whose mind was split several ways across time after his spaceship landed on Earth and exploded. His past selves hid various treasures to be found by his future selves (including multiple copies of The Mona Lisa!), which were to be sold off and used to get the materials to create a time machine so he could go back and prevent the explosion — something the Doctor might have helped with had he not discovered that the same explosion was the "lightning bolt" that stirred up the primordial soup to begin creating life on Earth...
• The Fifth Doctor story "Earthshock" is also an example. A human ship is sent back in time and causes the extinction of the dinosaurs, the dominance of Homo sapiens and the creation of the ship. (It also kills Adric, but that's beside the point.)
• "The Curse of Fenric" reveals that Ace only exists as the result of a stable time loop: she befriends her grandmother as a young woman, and when disaster strikes sends her to a specific address in London with Ace's infant mother.
• In the first season of the new series, the Doctor and Rose are followed everywhere by the words "Bad Wolf" — in the final episode, Rose saves the Doctor's life and uses the time-bending power of the TARDIS to deposit the words in the past, in order to inspire her to go forward into the future and save the Doctor's life, which ends in her putting the words into the past, etc., etc. The TARDIS-empowered Rose even declares that she's "creating herself" by doing this.
• This also crops up a few times in the second and third series (since the words were placed all over time and space, there's no reason for them to stop showing up just because they're not needed anymore), and more times than you can shake a TARDIS key at in the Ten/Rose Expanded Universe novel The Stone Rose. The phrase also turns at the cliffhanger of the Series 4 episode "Turn Left" (with all written words, from the Doctor's point of view being replaced with "Bad Wolf" — even the TARDIS' signage), in which it heralds Rose crossing over back into the main universe.
• "New Earth": Cassandra says her servant Chip was made in the image of her favourite pattern, which came from the last person to tell her she was beautiful, inspiring said pattern. That last person turns out to have been Cassandra herself in Chip's body, by the by, which also inspires Cassandra's murderous vanity.
• Used "for cheap tricks" (his words) in "Smith and Jones": when Martha first meets the Doctor, he stops in front of her on the street, takes off his tie, and walks off. When they meet at the hospital again, the Doctor can't ever recall meeting her. At the end of the episode, he goes back in time and takes his tie off in front of Martha in order to prove that the TARDIS is a time machine.
• "The Shakespeare Code" is a minor example — the Doctor quotes lines from Shakespeare's works to the man himself. Some of them he recognises, but some of them he hasn't got around to writing yet.
  • This is fairly common in the Historical Domain Character episodes. Donna gives Agatha Christie the ideas for Miss Marple and Murder on the Orient Express in "The Unicorn and the Wasp"; Amy inspires Vincent van Gogh to paint his famous paintings of sunflowers in "Vincent and the Doctor".
• In "Gridlock", the Face of Boe's last words, said with the Doctor and Martha present, are "You Are Not Alone." In "Utopia", Martha reminds the Doctor of the Face's message in the presence of Captain Jack Harkness. At the end of "Last of the Time Lords", Jack reveals that "Face of Boe" was a nickname he had when he was younger, implying that he will eventually become the Face of Boe after eons of Age Without Youth. As a result, thanks to what Martha said in "Utopia", Jack knows exactly what message he has to deliver, and what it means.
• "Blink" also repeatedly uses it. At one point, the Doctor pre-records his half of a conversation with Sally Sparrow; when Sally Sparrow has the conversation, it's written down, and the Doctor works off it to record his half. Also, his half is recorded as an Easter Egg on 17 specific DVDs; when the Doctor tells Billy Shipton (a cop sent back in time by the Angels) which discs to put the recording on, he's working from a list Larry and Sally have made in the future made of DVDs that have the video on them.
  Sally Sparrow: Let me wrap my head round this: You're reading aloud from a transcript of a conversation you're still having.
  The Doctor (on the video and transcript): Yeah. Wibbly-wobbly timey-wimey.
• Used in the canonical special "Time Crash", where the Fifth Doctor is brought forward in time and meets the Tenth. A problem develops which the Tenth Doctor instantly solves, working from his memory of when he lived through this very situation as the Fifth Doctor, watching his future self solve it. (This normally shouldn't work, since meeting an earlier version of yourself just results in the earlier version forgetting the whole thing, but Technobabble lifted that rule for once.)
  Fifth Doctor: You didn't have time to work all that out! Even I couldn't do it!.
  Tenth Doctor: I didn't work it out. I didn't have to.
  Fifth Doctor: [slowly dawning on him] You remembered.
  Tenth Doctor: Because you will remember.
  Fifth Doctor: You remembered being me, watching you doing that. You only knew what to do because I saw you do it.
  Tenth Doctor: Wibbly-wobbly–
  Fifth & Tenth Doctors: –timey-wimey!
• "The Doctor's Daughter": The TARDIS takes the Doctor, Donna and Martha to the planet Messaline because it's detected the presence of Jenny, the Doctor's Opposite-Sex Clone. However, the TARDIS arrives a bit early, leading to Jenny's creation in the first place.
• "The End of Time": The drumming in the Master's head is a signal planted by the Time Lords to escape their inevitable destruction in the Time War. They only know to plant the signal because historical records say it's there, and they realize it was probably them that did it. The Mad Oracle helps, as well.
• "The Lodger": The Doctor is temporarily stranded on Earth, and poses as a human looking for somewhere to live. Near the start of the episode he gets a room that was only available because the previous tenant was left a large amount of money in the will of an uncle he'd never heard of, and the Doctor reveals midway that he picked this building because there was a note telling him to beneath the building's ad. At the end of the episode, the Doctor tells Amy to write that note, while he goes back in time and changes the will.
• "The Pandorica Opens": The Alliance creates the Pandorica based on a book Amy read, which recounts the myth of Pandora's Box. Since the Pandorica is shown to transmit its signal to all time periods, it's implied to be the original inspiration for the myth.
• This is invoked in "The Big Bang", in which the Doctor is rescued from the Pandorica by Rory wielding the Doctor's own sonic screwdriver, given to him by the Doctor in the future after Rory rescues him. The Doctor then goes on to plant hints for Amelia to follow to resurrect her future self.
  
  This episode also features possibly the most pointless stable time loop ever conceived. Young Amelia is thirsty, so the Doctor jumps back in time several hours and steals a drink. He then returns to the present and gives the drink to her. The reason she's thirsty in the first place is that a few hours ago someone stole her drink.
  
  Given that Steven Moffat frequently writes in lines that poke fun at Doctor Who tropes (The Curse of Fatal Death is a long string of these!) this drink-loop is probably employed as an in-joke at how much the trope is being abused in this episode. In a later episode they acknowledge that they were only able to do all this time-looping because the universe was already collapsing anyways.
• In "Time", the second part of the 2011 Red Nose Day comedy special, we get three of these in as many minutes, two of which play this trope straight (Amy doesn't understand what her future self said, but still says it herself, even though the Doctor doesn't even explain it to her, and the Doctor waits for his future self to tell him which lever to use despite having no idea as the time loop is only a few seconds long) and the third of which justifies it:
  Present Rory: Do I have to remember all of that?
  Future Rory: It just sort of happens.
  Present Amy: [flirtatiously] Hi.
  Future Amy: [flirtatiously] Hi.
• As of "A Good Man Goes to War", the Doctor's name turns out to be one of these. The meaning of the word was apparently already established when he chose it, but due to centuries of crosstime adventuring, it turns out "doctor" means healer because of him. However, in some places, it means "mighty warrior" because of him.
• River Song:
  • Her whole existence is a series of these. She is named after herself (twice!), she is directly responsible for her parents hooking up, she's indirectly responsible for her being conceived in the TARDIS, etc. In "Silence in the Library"/"Forest of the Dead", the Doctor manages to save her imprinted memory because he figured his future-self wouldn't leave her to die, and his future-self, knowing that he didn't, thus created a way to save her...
  River: If you die here, it'll mean I'll have never met you.
  The Doctor: Time can be rewritten!
  River: Not those times. Not one line. Don't you dare.
  • In "Let's Kill Hitler", Amy and Rory make a Crop Circle as a dramatic gesture to leave a message in time to get the Doctor's attention. They were most likely inspired by River Song's various messages to the Doctor previously in the series. However, it turns out that their best friend Mels is River, and this is her first time meeting him as an adult. So this incident is probably where she got the idea for leaving unusual messages like this.
  • Heck, River's whole life is a giant time-loop. She only starting using her signature catch-phrase of "Spoilers!" after the Doctor used it on her the first time, having heard her use it a half dozen (or more) times before.
• Clara's life is yet another one consumed by this. She enters the Doctor's time-stream in order to save him, making her show up numerous times in his past. After he meets echoes of her in "Asylum of the Daleks" and "The Snowmen", he becomes curious about what is going on and finds the real her in "The Bells of Saint John", which leads to her travelling with the Doctor, and eventually ending up on Trenzalore with him with the opportunity to save him by jumping into his time stream. She says that she's not afraid to do it even though she knows she'll die because she's already done it — he already met her at the Dalek asylum and in Victorian London. This is despite the fact that the stars are going out and Strax is turning homicidal again, making this possibly the single most confusing example of time travel in the entire series.
• The 12th Doctor helps save Gallifrey in "The Day of the Doctor", and he was only able to exist due to the Time Lords changing history by giving the 11th Doctor a new regeneration cycle.
• "The Time of the Doctor" reveals that most of the Eleventh Doctor's run was one of these. The Church of the Silence (among other powers) besieges the Doctor on Trenzalore in order to stop him from using a crack in reality to bring back the Time Lords. After a few centuries of this, Madame Kovarian's branch of the Silence breaks away and goes back in time to try and kill the Doctor before he ever reaches Trenzalore, setting the events of Series 5 and 6 into motion. But, their attempt to blow up the TARDIS just creates the cracks that pose such a threat, and their creation of River Song to assassinate the Doctor just results in her saving his life multiple times, which means he lives long enough to get to Trenzalore to begin with. The irony is lampshaded by the Doctor when he pieces it all together.
  "You can't change history once you're part of it."
• Steven Moffat's general love of this trope led to the Series 8 cast referring it to as "The Moffat Loop".
• In "Time Heist", it turns out the Doctor was hired by the future version of Madame Karabraxos to carry out the robbery she herself witnessed and free the Teller.
• At the top of "The Magician's Apprentice", the Doctor abandons a young Davros on a battlefield upon realizing he will become the creator of the Daleks, his greatest enemies, realizes he may have created a terrible example of this trope in the process, and is willing to die to atone. But "The Witch's Familiar" reveals there is more to the story. The Doctor is able to recognize and rescue Clara, who is trapped within a Dalek casing, when she manages to beg for mercy. Why would Daleks have a concept of mercy? The Doctor realizes he instilled the concept in young Davros by rescuing him after all, as he should have done to begin with. He promptly heads off to do so.
• "Under the Lake"/"Before the Flood" has a stable time loop relating to what the apparent ghost of the Doctor was mouthing. "Before the Flood" even has an opening Teaser in which the Doctor breaks the fourth wall to lecture the audience on the general subject of the trope! It's even implied that the teaser takes place at the end of the episode!
• In "The Husbands of River Song", the Doctor creates a loop for River's sake. They crash-land on Darillium and she is knocked out cold. River told the Tenth Doctor back in "Silence in the Library"/"Forest of the Dead" that they had last met here, at a restaurant overlooking the Singing Towers. Now the Twelfth Doctor arranges for a beautiful restaurant to be built on the spot of the crash and then makes their dinner reservations! When she comes to he is waiting for her, looking as she describes him to Ten, and also gives her the sonic screwdriver that will allow her to live on in the library after her death. And they spend 24 happy years together before she heads off to her destiny.
• "Spyfall": When the Doctor reunites with her companions at the end, she's asked how she left instructions for Ryan on how to pilot Barton's plane without a cockpit. This clues her in on one last thing she needs to do, and she runs off to time-travel back to the construction of the plane and plant those instructions.
• The 2023 Children in Need skit has the Fourteenth Doctor accidentally crashing into the lab where Davros is building the Mark 3 Travel Machine, calling it a Dalek and referring to extermination before realising where he is and that Davros's assistant is writing this stuff down (although he was already thinking about anagrams of "Kaled"). He also accidentally breaks off the Dalek's multi-purpose claw, and chucks the assistant a sink plunger as a replacement.
• "The Giggle": This is the implication with "bi-generation" — when the Toymaker hit Fourteen with the Galvanic cannon to kill him, he didn't die, but instead accidentally pulled the Fifteenth Doctor to that point in time. At the end of the adventure, Fourteen decides to retire and stay with the Noble family and the revelation that Fifteen has a healthier head on his shoulders, the implication is that Fourteen will spend that time recovering emotionally and mentally, ultimately regenerate into the Fifteenth Doctor and get yanked through time to aid his previous incarnation.

With the show expanding into various other media formats, ranging from comics to books and audio dramas, various other time loops have emerged;

• In “The Guardian of the Solar System”, Sara Kingdom ended up travelling into her own past and having enough of an impact on Mavic Chen that he gave her the promotion that would bring her to Earth and get her tied up in "The Dalek Master Plan" in the first place. Though it's not outright confirmed, Sara also theorizes that her ranting to Bret about Chen's corruption might have given him the idea that he could trust her when he turned traitor, directly leading to her killing him in that story.
• “Second Chances” sees the Second Doctor’s currently-amnesiac companion Zoe regain her memory of a trip to a particular space station in what was her home era's future just as the event is about to happen 'now'; she ends up ensuring the survival of her past self during the crisis while trying to save the station.
• “Luna Romana” is the result of the Doctor’s old enemy Stoyn luring the Doctor to ancient Rome by stealing the TARDIS and going back in time to plant a piece of the Key to Time there over a year ago, meaning that Stoyn lured the Doctor in using material he only acquired because of the abduction. On top of that, Romana escapes Stoyn’s trap by sending herself back in time so that she can then be in a position to tell herself to go back.
• “Cobwebs” sees the Fifth Doctor join his old companion Nyssa’s attempt to investigate the outbreak of lethal plague Richters’ Syndrome. However, as a result of the TARDIS crew going back in time to trace the origin of the plague, they end up unwittingly causing the Richters’ outbreak that Nyssa was investigating in the future.
• “The Butcher of Brisbane” features journalist Ragan discovering his future self’s corpse, thus beginning the chain of events that lead to him being sent back in the first place as he investigates rumours that Magnus Greel is using time travel to dispose of his enemies.
• In the Past Doctor Adventures novel “Imperial Moon”, the Doctor reveals the existence of in the TARDIS’s time safe, which he describes as a permitted temporal paradox; items are put in the safe in the future so that they can be received in the past. In this case, the item in the safe is a diary of an expedition to the Moon by the British Imperial Spacefleet in 1878, which prompts the Doctor and his companions to go back to that time and place once the diary reveals that the Doctor and Turlough met that expedition on a specific day. The Doctor’s role in the expedition concludes with the Doctor receiving the diary so that he can leave it in the safe and set himself on the path to experience these events.
• In “The Wrong Doctors”, the Mardacks are a race of business consultants who have come to the pocket dimension the current crisis takes place in due to them detecting Phalanxium. However as Phalanxium decays backwards, the Doctor realises that the Mardacks are actually the source of the Phalanxium they detect; they’ve been detecting the residue it left on their bodies after they were killed in an explosion.
• “The Last of the Cybermen” is one big one. Frank and Lanky actually recognise the trio of the Sixth Doctor, Jamie and Zoe from ten years ago and are playing along to maintain the timeline. They first met them ten years ago when they travelled back from the present with the Cybermen. The last great strike on Telos was actually the Cybermen's own rescue fleet from the future forced to ram the planet by Findel, who merged with the Cyber-Planner in the future. In the end, the only reason the Second Doctor came to the planet in the first place was because of a mysterious message he received from his Sixth self.
• When Henry Gordon Jago is travelling with the Sixth Doctor in “Voyage to Venus”, he ends up teaching the ancient Venusians the tune of "God Rest Ye, Merry Gentlemen", which explains how the Third Doctor would later call the tune a "Venusian lullaby" during his visits to Peladon.
• “1963: The Assassination Game” sees the Doctor and Ace come back to 1963 when they discovered, in 2013, veiled references to themselves showing up again in 1963 in the autobiography of their old ally Group Captain Gilmore of Counter Measures. The Doctor has to explain to Gilmore that history's not immutable and Gilmore's not invincible, though.
• In “Loving the Alien”, the Doctor’s enemy George Limb becomes fixated with trying to evade his predicted death by luring in the Seventh Doctor and Ace and shooting Ace as bait for the Doctor. Limb claims that he intended to go back and change this once his own death had been prevented, but the Doctor insists that Limb can’t stop himself killing Ace but at best just change his position relative to what happened.
• “The Eight Doctors” concludes with the revelation that the Eighth Doctor was allowed to visit his seven past selves by Rassilon himself, Rassilon using the Doctor to tie up some "loose ends" in the timestream, ranging from convincing the First and Second Doctors to take a particular course of action to saving the Third to Seventh Doctors from traps or attacks by their various enemies.
• “War of the Daleks” reveals that several of the Daleks’ encounters with the Doctor have been an attempt to create one while essentially tricking history; having found evidence during their invasion of Earth that Davros would destroy Skaro in the future and Earth’s past, after failing to outright change history, they create an elaborate scenario where Davros will be awoken on a planet that he thinks is Skaro and thus go on to destroy that planet, preserving the historical evidence without actually losing their homeworld.
• "Vanderdeken’s Children” features a derelict ship that has no beginning, but been traveling in an endless time loop through the same series of events forever.
• Two different stages of the Master’s life only occur because of his future self setting them up; he is reduced to his burnt state because his future self attacked him to set up a scenario he already experienced (“The Two Masters”) and he is granted a new set of regenerations by his own future self when the future Master already has those regenerations (“Day of the Master”).
• In “The Lost Dimension”, the Eleventh Doctor’s investigation of a new dimension destroying the prime reality results in him unintentionally creating the very catastrophe he was investigating.
• I. M. Foreman in Interference became a wanderer leading a sort of freakshow of his own increasingly bizarre and inhuman regenerations after finding them all lying amnesiac in the Gallifreyan wastes. Book Two establishes that they were there because towards the end of the story, in which his final regeneration bonded with an entire planet, he took his proto-TARDIS caravan back to Gallifrey with the others and it exploded, depositing them all in a heap exactly where he would find them and causing enough harm to force them all to move on to the next regeneration. (Ironically enough, while Foreman's adventure is a stable loop, the events in question lead to the Third Doctor regenerating at the wrong time, thus causing an entirely separate set of timeline issues.)
• From the Doctor Who Storybook 2007, the short story "The Cat Who Came Back". During Rose's childhood, a cat wanders into Rose and Jackie's apartment. Despite many attempts to get rid of it, the cat stays and they give in, with the cat living for five more years. This cat turns out to be Mitzi, the first cat in Hyperspace, who Rose and the Tenth Doctor encounter in the future on the planet Phostris. Recognizing her pet, Rose and the Doctor go back to the Powell Estate and drop Mitzi off, who goes on to live with Rose and Jackie, being renamed Puffin.