One has successfully Tricked Out Time when they can say they've "faked" a Stable Time Loop, thus avoiding Temporal Paradox. Instead, the result is a Close Enough Timeline.
How does one fake a Stable Time Loop? Well, you go back in time, and you make it look like the original thing happened, when instead, something else happened entirely. The important thing is that everyone who witnessed the event to be changed still see the same thing. Care must be taken to ensure the change is not detected by the wrong people until after the original time excursion point. If you go back and savesomeone by replacing them with a robot clone at the last minute, it's probably best that this person go with the time traveller Back To The Future™.
This also works for prophetic visions: eg. a character who sees himself falling off a cliff to his death in a crystal ball may decide to stage the same scenario under conditions where their safety is ensured.
See also You Already Changed The Past, where any change you make to the past already happened before you thought of it. If a paradox IS possible, but you avoided it by making it look like you haven't changed anything, you have this trope. If you think you've Tricked Out Time, but actually You Already Changed The Past see Mind Screw.
Steins;Gate Rintaro relies on such trickery to save the world, save the girl and the like.
One Dexter's Laboratory comic book featured Dexter finding a copy of that very comic book. He flips to the end and finds a scene in which the rest of his family mourns his death. He saves himself by getting his family to act out that scene.
Booster Gold: Booster has done this twice: once in the comic 52, in which he fakes his own death by retrieving his future corpse and replacing himself with it (with the help of Rip Hunter). The second time was in his own comic, in which he prevents Ted Kord's death at the hands of Maxwell Lord with the help of three other Blue Beetles. Unfortunately it doesn't work, and he returns to the present to find it's a Bad Future. However, Beetle himself seems to have found a way around this as Wordof God confirms that it is him in his old lab at the end of the issue.
In Justice Society of America, the Hourman of the 853rd century pulls the original out of the battle where he died and replaces him, using holograms to disguise himself. It gets better, because that villain is the same who "killed" him the past, when he replaced the original Hourman. His team-mate Atom-Smasher does a nastier one with the same villain, switching him in for his mother on a doomed airplane flight.
In Don Rosa's Of Ducks and Dimes and Destinies it is revealed that Scrooge McDuck got his first dime not from the man whose boots he cleaned, but from Magica De Spell, who tried to steal the coin from Scrooge when he was just a child. She then realized that the coin would be useless to her if Scrooge didn't have the coin while becoming the richest duck in the world.
In Fantastic Four: The End, set in a possible future flashbacks give the idea that the children of Reed and Sue died in a catastrophic explosion going up against Doctor Doom, only to find out that the magical device being sought by Susan Richards allows for them to pull everyone into their present leaving it to only appear that everyone died in the explosion and preserving the timeline without spawning any alternates.
In one Jughead's Time Police story, Jughead gets a message from his future self to save Riverdale from a flood. However, eight centuries later, it's a historic fact that Riverdale was hit by a flood. How can Jughead save Riverdale without altering history? Since the 'fact' is based on a headline dug up by future archeologists, all Jughead does is create that headline to be dug up later. That way, he can avert disaster without changing the future.
'Jughead: Since we can't change history, we'll have to fool history! It'll be the con job of the century! Er, I mean centuries!
In Harry Potter and the Methods of Rationality, Dumbledore freely messes with time in this way in order to keep from messing with time in ways that create a time-wasting paradox. When preparing for a trip which may involve doing something that he doesn't yet know will cause a paradox, he casually glances at a specific brick in a wall. If there is a note taped to the brick that says "NO.", he cancels his trip and instead goes back just long enough to leave the note before going off to figure out why he had to cancel the trip.
Harry did something similar by accident. He tried to answer a math problem by forcing a time loop that would stabilize only at the correct answer, and all he got was a note saying Don't mess with time travel. He then planted the note and resolved not to come back to that research for a long time.
Discussed in Kyon Big Damn Hero, where Kyon points out this possibility to Mikuru. It hasn't actually come up in the story yet, but given all the time traveling involved it almost certainly will at some point.
In Back to the Future, Doc does this by wearing a bullet-proof vest when the Libyan terrorists shoot him. He doesn't tell Marty this until after Marty comes back. The plot of the entire film is a semi-successful attempt to do this, since Mr Baines still doesn't hit George with the car, but the timing of major events in George and Lorraine's relationship post-dance is otherwise the same (they live in the same house, have the same number of children at the same time with the same personalities and so on).
Back to the Future Part II, when Doc and Marty go back in time to stop "young" Biff from getting the Gray's Sports Almanac. Doc warns Marty not to interfere with Biff receiving the almanac from his older self, because they had to make "old" Biff believe that his plan worked so he'll return the time machine (which he stole from Doc and Marty earlier) back to the future where they left it.
Marty suggests in Back to the Future Part III that they bring Clara Clayton back to the future with them - which would remove her from 1885, where she's supposed to be have died by falling into "Clayton Ravine". Doc rejects this as a step too far - but the filmmakers have suggested that if Doc had appeared to go over the edge of the ravine when the train crashed Clara may have killed herself by jumping into the ravine, removing herself from the timeline and causing it to be named after her after all.
The filmmakers do state that Doc himself created a Tricked Out Time situation with the Clayton Ravine in the first revision to that timeline: originally, Clara's carriage went over the ravine, resulting in the name; in the revised timeline where Doc saved her (but where Marty was never present), she committed suicide by jumping into the ravine after Doc was killed by Buford, resulting in the name. This is used to explain why both Doc and Marty know of the ravine by that name.
Millennium: people from the future fill up their population by studying records of who dies in plane crashes, then sleep gas the plane and "borrow" the would-be casualties, replacing them with fake bodies. Notable that they eventually screw up, and the resulting Temporal Paradox blows up most of the local Time-Space Continuum.
In Primer, one character recorded all of his conversations on a previous iteration of the time loop and listens to them on his earpiece to keep the loop as stable as possible...except for the one variable he wants to change.
In Freejack, future people perform kidnappings from the past so their wealthy clients can extend their lives through Grand Theft Me. They capture their target right before he or she would have died, and explicitly choose only targets who would have died in ways that leave few or no clues behind, such as massive fires or explosive car accidents.
In Edge of Tomorrow, once Cage kills the Omega, he gets soaked in his blood and again goes back in time. Only this time, it's the day before the one he lived endlessly through a "Groundhog Day" Loop - and the Omega is already dead.
One Time Patrol story by Poul Anderson has a Patrol member intentionally looking away as his girlfriend falls into a waterfall, precisely so he can come back and rescue her later.
In Robert A. Heinlein's The Number of the Beast, the protagonists rescue Long's mother by traveling back in time and swapping her body with a brain-dead clone, seconds before it is hit by a truck. It's made even more Timey Wimey Bally by the fact that Long gets the idea to do it by going back in time and filming himself doing it.
Invoked repeatedly in The Science of Discworld books, especially the third book in which the UU wizards and the Auditors of Reality have a mini-Time War over The Origin Of Species that will decide Roundworld-humanity's fate.
This is the whole point of Night Watch: Past Sam Vimes's mentor dies too early, so future Vimes must stand in and take his spot mentoring himself. As long as he gets it close enough, everything will snap back into the way things were before the past was messed up.
In Captain Underpants, George and Harold go back in time to grab something that was destroyed before it was destroyed, replacing it with a replica.
Used once in Perry Rhodan to retroactively save a species that had been wiped out in an early arc of the series. With the aid of a species of ghostlike natural time travelers, they were snatched from their moments of impending doom and brought forward to the then-present day instead; since either way they no longer existed in the past to affect it, history proceeded unchanged and paradox was averted. note This was a one-time event; the 'timewalkers' by and large had an aversion to the 'border time' because, apparently, going past it further into the future even by accident would cause them to cease to exist. What exactly — other than the readers' perspective, of course — made specifically the series' current modern day so critically distinct from any other arbitrary potential 'present' on the timeline was never really addressed.
Das Königsprojekt: A different approach was taken in this German novel. Here, it is possible to change the past - but only if there are no written sources of the event changed, or so few that you can change them on the fly - for example, giving a noble family a lot of diamonds and correcting the only source, the family chronicles, from "the fortunes of family X were greatly reduced during [the time in question]" to "augmented". Killing Martin Luther (because the only existing time machine, built by Leonardo da Vinci, is in the hands of the Catholic church) is right out and has to go awry, as they found out when they tried one time. (The time traveler and the machine returned with a bang to the present, resulting in the story of Martin Luther throwing an inkpot at what he believed was the devil.) Fridge Logic: What happens if there are no sources in the time traveller's present, but many at the point in time he's going to?
In Eoin Colfner's Artemis Fowl: The Time Paradox, the paradox comes from the fact that things are happening to Past!Artemis that Present!Artemis doesn't remember. Turns out No.1 erased his memory and replaced it with what Present!Artemis remembers. Past!Artemis later wakes up thinking "something about fairies," creating a double Stable Time Loop.
In Time Riders by Alex Scarrow, "The Agency" recruits people at the moment of their death in order to fix history when it is tampered with.
In the Bad Future of the Star Trek: Millennium trilogy, the Ascendancy is out to literally destroy the universe, and the Federation's last hope for preventing this is to destroy Bajor. They can't get there now, but they can in the past; however, if they change the past they'll just create an Alternate Timeline, doing themselves no good. Admiral Picard's brilliant solution is based on this trope: plant "deep-time charges" on Bajor in the past, leave them there until the present, and then detonate them. Unfortunately, the Ascendancy finds out and goes them one better...
Live Action TV
The The Sarah Connor Chronicles episode "Self Made Man" is a text book example of this trope. In it, a terminator sent back in time to the year 2010 to assassinate the Governor of California during the re-opening ceremony of an historic building in downtown LA accidentally arrives 90 years too early, inadvertently disrupting the chain of events which were to lead to said building's construction in the first place. The terminator then spent the next several decades building his own real estate enterprise from the ground up for the sole purpose of ensuring the construction of this building would proceed as it would have without his original interference. He then proceeded to hibernate in one of the building's walls, gun in hand, intent upon carrying out his mission as originally planned. Luckily, Cameron stopped him.
In the Star Trek: Deep Space Nine episode "Past Tense", Sisko impersonates a man who was supposed to lead a historically significant riot, but died trying to protect him.
This led to a recurring gag as Starfleet soon calls up Sisko wanting to know exactly why the history books now show pictures of him in the 21st century, and characters like Bashir and Nog keep noticing Sisko's photograph whenever they're reading about Earth history.
Another episode had a Bajoran poet who traveled centuries into the show's present listed as having disappeared at the time he traveled until after his visit, and then all of the histories were updated to include what he did later after he went back. Sisko concluded that the wormhole aliens that caused it were screwing with them.
The new series episode "Father's Day" is all about this trope. You can visit the exact same point in time repeatedly so long as you don't make your past self experience something you don't remember experiencing.
Though not part of any of the TV series, this would have added an interesting angle to the Doctor's position in the future episode "The Fires of Pompeii". He's in denial about why he can't try to save the city.
Major spoilers: Series 6 ends with the Doctor going to the death we saw at the beginning of it... inside the shape-shifting robot from "Let's Kill Hitler", disguised to look like him.
This seems to be the M.O. of said shape-shifting robot. It goes back to near the end of the life of a Karma Houdini, painfully tortures them to death to pay for their crimes, then impersonates them for what remains of their life. As far as the history books are concerned, nothing has changed.
The Doctor Dances has a minor one. When the Doctor blows up the Chulan warship ( which is an ambulance) he mmentions that "History said there was an explosion here". Originally, this was caused by a bomb, but Captain Jack got rid of that.
In the audio dramaThe Fires of Vulcan, the Fifth Doctor is told by UNIT that his TARDIS is found in Pompeii, buried under the volcanic ash and revealed by an earthquake. Later, as the Seventh Doctor, the TARDIS drops them in Pompeii, and the Doctor is initially resolved to his fate of dying there. They eventually figure out a plan involving letting themselves get covered in ash, and then jumping forward to just before the Earthquake, letting the earthquake happen, get out, and let UNIT find the TARDIS, and then go and steal it back.
The novel War of the Daleks undoes the destruction of the Daleks' homeworld Skaro by having the Daleks discover a piece of centuries-old footage describing the events, which begin with the discovery of their creator, Davros, on Skaro. They travel back in time, find a suitable planet that looks a bit like Skaro, move Davros to it, and fake the rescue mission that discovered him — so the film remains accurate, but a different planet got blown up. The book wasn't particularly well received, since the description of this complex retcon took up a lot of space that could have been used for actual plot. The retcon itself is generally filed as Fanon Discontinuity by fandom but it would seem that new series expanded universe material sees otherwise, for The Adventure Games: City of the Daleks features the first visit to a post-Time War Skaro, mostly intact after all those years.
Another (hilarious) example is the audioplay "The Kingmaker". A wildly complex sequence of events leads to William Shakespeare hijacking the TARDIS so he can convince Richard III to kill his nephews and ensure that history remembers Richard as a monster and the Tudors (Elizabeth I's family) as heroes. It eventually ends up with Shakespeare being killed at Bosworth Field, and the Doctor dropping Richard off in the Elizabethan era with a copy of the complete works of Shakespeare...
In Heroes Volume 5, Hiro is finally able to save Charlie and tricks his past self and past Ando into doing what they did originally to avoid a Temporal Paradox.
Arnold Rimmer does this unintentionally in Red Dwarf. After Lister changes his past so that he is a multimillionaire inventor (of a product previously invented by a childhood acquaintance of Rimmer's) who never joined the Space Corps, Rimmer conspires to use the same time travel method to inspire his own young self to invent the same product so that he will be the wealthy tycoon who has sex with beautiful women. Unfortunately, the inventor of the product from the original timeline is within earshot and apparently beats young Rimmer to the punch, effectively returning everything to the way that it was. Except that Rimmer is still alive. Then he accidentally blows himself up.
The "prophetic vision" variant was used in the Painkiller Jane: A neuro had a vision of a future where he shot and killed each member of Jane's team when they pursued him and warned her against chasing him, trying to stop this. It came true anyway, with one small exception: Jane was the one who took the shots, carefully disguising herself so she appeared to be each member of the team in turn. Since she has a Healing Factor, no one died.
This is the standard way to resolve a paradox caused by Narcissists in the Tabletop RPGContinuum. Worthy of note is the fact that Continuum ideology is that all apparent paradoxes are inevitably resolved this way, and that no real change in history has ever existed or can ever exist. Since causing temporal paradoxes is a main form of time-traveler combat, hypnotism is a survival skill and major historical figures have understudies.
Also worthy of note is that crasher (the aforementioned Narcissists) philosophy, any change results in creating a new paraverse, and that the Inheritors are brainwashing Continuum spanners into keeping the universe they are currently occupying unchanged, fueling the crashers' desire to escape.
One wonderful example of tricking out time through Loophole Abuse is presented in the book: The GM tells one of the PCs that he has a message on his answering machine describing exactly where, when, and how the PC will die. The PC merely goes back in time a few minutes and leaves himself that message as a prank. The message had to be left; nobody said it had to be true.
The old GURPS supplement Time Travel featured a time agency that worked off the principle that it didn't happen unless someone from their present saw it happen. As noted in other examples, looking away when a friend is about to die is standard operating procedure as it leaves a loophole that may allow them to be saved. Many missions involve standing in the crowd at a historical moment so as to watch it happen and "fix" it in place against future tampering.
In Chrono Trigger, the hero is fried by Lavos the Eldritch Abomination. But wait! At the festival that began the game, there's a minigame where you can win a handy Clone. The heroes take the clone, go to the point precisely before you know who was evaporated, stop time, and replace him with the clone, then take him back to the future.
In the first Suikoden game, the hero's friend/servant sacrifices himself by locking himself in the same room as a flesh-eating fungus to save the hero. When the hero gets back to the room, no trace of the servant remains; it's assumed that he was completely consumed. However, if you get all of the Stars of Destiny, it's possible to time travel back and whisk him back to the future; his disappearance being explained that way.
Ghost Trick: Sissel has to do this multiple times to trick Yomiel into believing that Cabanela and the pigeon-headed man have been murdered. Yomiel knows about ghost tricks, so Sissel has to hide both himself and the fact that their corpses are still alive, or else Yomiel will just kill them in a more confirmable way.
Dragon Quest V has the main character sent to the past in order to retrieve a mystical orb he owned when he was younger until it was destroyed. This particular act can actually be either this or You Already Changed The Past depending on whether or not you approach the grown version of yourself while still a child in the beginning. Any other attempts to mess with the past (such as preventing your father's murder) are doomed to failure, since you have no way of pulling that off without anybody seeing your interference.
World of Warcraft has a series of dungeons called the Caverns of Time, each of which involves a different past event from previous games or lore. In every case adversaries throw history off the rails and it's up to the group to set things right - or at least, close enough. Laser-Guided Amnesia makes certain that the original apparent history remains, whether it happened or not.
One of those is "The Culling of Stratholme" where you have to assist Arthas wiping out the infected population that is being turned into undead by the Scourge as the Infinite Dragonflight attempts to kill him so he won't go to Northrend and become the Lich King. Fridge Logic suggests it would be a good idea to allow one of Azeroth's greatest monsters to die before his Start of Darkness, however Hitler's Time Travel Exemption Act seems to apply to his dark genesis.
The canon reason for letting The Culling go as written in history, was that without it, the undead forces would have gotten a massive increase in their forces from the denizens of the city, and would have been far stronger in the final battle on Mount Hyjal, winning that fight.
The Time Police Deep Time take this trope and run with it. They can't kill (most) anyone in the past, since that will affect the future, but they can, for example, send one of their female agents back in time to be the first girlfriend of a male guard. Then she tries to get past him, and he can't bring himself to shoot her. They do this to about half the crew. One poor bastard got his father replaced with a Deep Time agent.
"I've always been proud of you. Sorry I pretended to be your father for the past thirty years so I could get past this door."
Memnon does this with A2-Z when he needs the computer to calculate a particularly complex Starslip path. He drops A2-Z off in the 20th century, replacing the first, primitive prototype of A2-Z with its own future version, and then instructs it to spend the following centuries secretly working on the problem while hiding its advanced status from everyone until the day Memnon returns to the future. Subverted — it still wasn't enough time to find the answer.
Homestuck: Played with. Appearifiers can snatch people and items from other points in time, but only if they've played out their part and have nothing important to do, which would cause a paradox. If that would be the case (for instance, Rose attempts to Appearify Jasper before he can tell his terrible secret) the machine instead generates an ectoplasmic ghost image... which can be used to extract genetic material to create a clone of the original. But the clone is almost always mutated and damaged in one way or another... and when it's actually a perfect copy, that means it's destined to be sent back in time and turn out to be the original in a complex Stable Time Loop. Confused yet?
The nature of time in Paradox Space will not allow any alteration to the Alpha Timeline; any significant change will create an offshoot timeline doomed for deletion. At best, someone from a doomed timeline can send something back to the alpha timeline insure that the alpha timeline happens. Tricking out time is the only way to succeed in any Time Travel shenanigans.
Bob and George: at the end, in order to ensure the timeline is intact for the X and Zero games, including the Cataclysm, all the characters fake their deaths and move to Acapulco. This should be noted as one of the few times anyone in Bob & George gave a damn about the timeline, which had been twisted, warped, set on fire, run over by a steamroller and blown up with many, many elaborate time travel shenanigans before that.