11/22/63 gets...vague with how time travel works. At first at seems like traveling to the past always creates a fresh new timeline, or "string," where none of your other trips happened, and if you screw something up, you can always make a new string where you didn't. However, it turns out that the strings can become tangled if there are too many of them, and making changes to history is like plucking the strings, causing them to "harmonize" with each other. If you get too many strings harmonizing, time itself will shatter from the vibrations. Jake nearly causes this to happen by saving JFK's life, but somehow he's able to save the world by making another string where that doesn't happen. All of this is explained by a hobo who's been driven insane by a very nasty version of Ripple-Effect-Proof Memory (imagine remembering hundreds of different futures all at once, all in equal clarity) so there's a lot the reader never finds out.
Poul Anderson's Time Patrol stories are historically well-researched and confusing. Among other things, the future is "uptime" and the past is "downtime," which makes it sound counterintuitively like time is a river that flows uphill. (This is consistent with convention in geology and archeology, where an earlier period is "lower" because its evidence is in deeper strata.)
In the 1632 series, the Grantville inhabitants from 2000 are "uptimers," the seventeenth century natives are "downtimers."
The End of Eternity uses words like "downwhen", "upwhen", "anywhen" and "everywhen".
Animorphs made use of Time Travel occasionally, and each time it apparently worked differently. Different techniques of Time Travel were involved, at least one of which was by use of a thingy created by the closest thing to a God in the series, and another (a Bad Future-esque thing) was just flat-out never explained. The bad future was apparently a dream caused by an advanced being for some reason. Maybe.
Eoin Colfer's Artemis Fowl and the Time Paradoxdoes not actually feature any paradoxes. The prequel on the other hand... Specifically, an island was magically removed from normal time for 10,000 years, but the magic is breaking up and time starts running alternately forward and backward at varying speeds. Holly dies, but Artemis fires a shot backwards in time thus killing the demon who killed her and bringing her back to life. Furthermore, Artemis goes back in time and causes a mosaic of himself to be created hundreds of years in the past, a fact which is only noticed in the present day after he gets back. Artemis questions the first paradox, but eventually gives up trying to figure it out.
In Last GuardianOpal defies Stable Time Loop by having her past self from Time Paradox killed, and manages to survive. What Opal's timeline looks like now is anyone's guess.
The Book of All Hours duology by Hal Duncan doesn't even try to claim to be otherwise. It's such a mishmash of pocket universes, alternate universes, and paradox that causality can't even be seen with a telescope on a good day. Essentially: think of the universe as a huge piece of vellum on which reality has been written. Then crumple it up. Most characters make such a habit of going not just back and forth in time but sideways that one goes back to the day where he, as a child, met his elder self, and that elder self committed suicide... only now, as the elder self, shoots his younger self instead. Nothing happens to the elder.
Date A Live has this thanks to the existence of Kurumi. A notable example occurs in the tenth and eleventh volumes. Origami (now a Spirit) has Kurumi send her back in time so that she can prevent her parents from being killed by a Spirit. Origami gets into a fight with another Spirit and one of her own stray attacks hits her parents' house. The revelation that she was the one responsible for her parents' deaths causes her to enter Inverse Form. She returns to the present (as Kurumi's power has a time limit) and causes massive destruction. Kurumi then sends Shido back in time in an attempt to prevent this. Shido initially fails but does comfort Origami after the fact, resulting in her obsessive love for him in the future. He then finds Kurumi's younger self and has her send him further back, allowing him to stop Origami from killing her parents. This creates a new timeline where Origami's parents still end up dying but in a traffic accident, so Origami no longer hates Spirits. However, she nevertheless inherits the power and personality of her original timeline's Inverse Form, which manifests as a split personality. Eventually, Origami's two personalities fuse into one, while the other Spirits also gain memories of the previous timeline.
In Thief of Time, it's revealed that, following various alterations to the Disc's temporal dimensions, the "true history" barely exists, and their main job is to prevent the Timey-Wimey Ball from imploding.
In Night Watch, when Vimes travels thirty years into the past to become his own mentor, even the monks aren't sure what's happening.
Lu-Tze: For a perfectly logical chain of reasons, Vimes ended back in time even looking rather like Keel! Eyepatch and scar! Is that Narrative Causality, or Historical Imperative, or Just Plain Weird?
If you try to place the times and events of some books, you will find they take place a couple years before a different book, and at the same time, hundreds of years before the IMMEDIATE SEQUEL of that different book.
Sir Terry himself at one point explained that "There are no inconsistencies in the Discworld books; occasionally, however, there are alternate pasts."
Dirk Gently's Holistic Detective Agency: Significant plot points hinge on characters being able to change the past (the villain wants to stop life evolving on Earth, and as part of the attempt to stop him, Dirk interrupts Coleridge when he's writing "Kublai Khan", the full text of which was previously established as existing in that universe). But the pay-off to the background gag of Richard's sofa hinges just as much on being a Stable Time Loop. This is during the same trip through time.
Jack Chalker's Downtiming the Nightside: People leaping through time can affect changes. If the change is small enough, nothing much happens to the timeline, but significant changes can happen. Karl Marx is killed 3 different times, at 3 different points of his life. At the end of his life, not too significant. After he publishes Das Kapital, not too bad either. Before he publishes it on the other hand... And this is just the tip of the timey-wimey iceberg.
The Dragonriders of Pern novels by Anne McCaffrey have time-travel courtesy of a side-effect of how the dragons teleport themselves and their riders all over the planet. However, you can't change the past. Several story lines, especially in the original novels to do with solving the empty weyrs, rely on the fact that major characters go back in time to make history happen, usually inadvertently. Meanwhile, coming close to yourself causes mental confusion. This happens to Lessa at least once and, of course, it drives the plot.
René Barjavel's novel Future Times Three is one of the first books to describe the Grandfather Paradox, and contains an appendix describing how the victim of the paradox is constantly oscillating between existence and non-existence. But there is also the case of an old servant who was saved from death by her bosses through time travel, who the hero does not remember having met because he visited the house before they went back in time to save her... and the servant seems to remember somehow that she should have died. Also, characters living during a war where common necessities are scarce are using Mental Time Travel to go back in time before the war to buy any supply they run out of in the present (which should mean that at one point in the past their cupboards must have been bursting with supplies).
It gets even worse in Harry Potter and the Cursed Child, where despite what was previously established, Albus and Scorpius' time travel does change the timeline. Scorpius mentions "Professor Croaker's law" which apparently sets the furthest someone can safely travel back in time at five hours; presumably further travel cannot form a stable loop. This is compounded further when, after the first two acts clearly and unambiguously show that travel to the past creates alternate timelines, the climax depends on another Stable Time Loop: The villain and heroes travel to the past. The child heroes have no way of stopping the villain from changing time, thus preventing the Good Present that they know and love. Their solution is to send a message forward in time to Albus's father Harry. Harry gets the message and goes back in time to stop the villain's plan. Without Harry coming back in time, the villain would have succeeded in changing time so that the timeline in which Harry got the message never existed. Summarily, the only way for Harry to know to come back to the past was for Harry to come back to the past. Under the time travel methodology established earlier in the play, as soon as the villain and heroes travelled back to the past, all of time from that point forward should have changed, and adult-Harry never should have existed.
Haruhi Suzumiya. The first thing we hear about time travel is that it's like a picture book; it looks continuous, but it's not, and scribbling on one page won't change the ending, so it's impossible to change the future. That gets thrown out the window pretty quick, with time loops up the wazoo. Several space-time locations get multiple time loops overlapping over them at the same time. However, starting in Novel 9, the timeline splits— not diverges, splits— and later fuses back together, and in novel 10 it is revealed that the evil time traveler Fujiwara is from a different future than Mikuru. In his, she's dead—and he wants to fix that, because she's his big sister. Unfortunately, in the timeline she's from (where she survived), her little brother never existed in the first place. So it's possible to change the future, right? Maybe. Because when all this craziness is going on, Kyon brings up the picture book analogy again, and it's confirmed that that is how time travel works (though at the same time it's implied to be an incomplete explanation). The mechanics of time travel in The 'Verse are incoherent now.
Heinlein wrote a short story called By His Bootstraps, in which the protagonist exploits a time machine to move himself forward in time. Simple enough. The Mind Screw comes in when he does this by his future self sending back his intermediate self to persuade his past self to enter the machine's portal. When the past self becomes the intermediate self, he attempts to double cross the future self, but that double cross naturally results in him becoming the future self. Follow all that?
For a real, double whammy version of mind screw, read —All You Zombies—which chronicles a young man (later revealed to be post-real-sex change) taken back in time and tricked into impregnating his younger, female self (before s/he underwent said sex change); then he turns out to be the offspring of that union (time-relocated yet again), with the paradoxical result that he is both his own mother and father. As the story unfolds, all the major characters — the young single mother, her seducer, the alcoholic writer, the bartender who recruits him into the time-travel corps, and even the baby — are revealed to be the same person, at different stages of her/his life. How's your mind doing now?
In Johnny and the Bomb, Pratchett explains that most time travellers forget the original timeline when they return to the new one because of the human tendency to accept what's around them as normal; but if you really try (or are reminded of it by some useful clue) you can remember how things used to be.
Of all the complications she regularly found herself in (and that was a hell of a lot of complications), she liked time travel the least.
Dean Koontz averted some time travel issues in Lightning by virtue of having the Nazis invent time travel, the limitation being that it can only send you forward (and then you snap back to your point of origin when you make the return trip). While this has its own problems, it at least eliminates the ability to murder your mother before she gave birth to you. You cannot change your own past, but you can change the past of anyone born after you so long as the changes you try to make are not contradictory, and you can bring objects back. Played straight in that if a contradiction is demanded, the portal will refuse the forward transfer (this gets the heroine killed in one timeline). "Destiny struggles to reassert the pattern that was meant to be." Sometimes happily, and sometimes not so happily, it succeeds.
David Gerrold's The Man Who Folded Himself features a time-travel belt, which has the traveller completely paranoid about the possibility of a Temporal Paradox destroying him. It turns out that Temporal Paradoxes are impossible; Time Travel rewrites history except for the guy who travelled through time. Various Mind Screw moments: the protagonist has orgies with himself of different ages, writes himself out of history, has a family with himself as a female, eventually has that written out of history (but his son still exists) and culminates in finally giving himself (as the son, so he's his own father) the time travel device. On the last, the idea of where it came from is explored a couple of times and eventually it's hit upon that it's impossible to know where it came from, the creators must have been written out of history. Oh, and he kills Jesus at an early age. It's okay, he goes back and stops himself after finding out how much it screws with history.
The Never Again series starts out simple enough. It seems to follow the many-worlds interpretation of quantum mechanics so that time travelers can do anything they want, but will create a new timeline that never intersects with the old. Then comes the third book, where that is thrown out the window, and the author's attempts to explain what is happening (with a lot of Technobabble about "intersecting universes" and the like) just raises further questions.
The character of Phanthro in Relativity is a time-traveller from the distant future. He's constantly altering history (for the fun of it). When he's asked how he can alter the past without wiping his own time period out of existence, he just says, "Time doesn't work that way." No further explanation is ever given.
Harry Harrison's The Stainless Steel Rat Saves the World features two overlapping timelines (one of which only has a temporary existence) and a loop. The lead character travels back in time to stop the Special Corps being removed from history, and manages to disrupt the enemy's plan. He then follows them further back in time, landing in an alternate history where Napoleon conquered Britain. He messes up the controls on the enemy time machine, and (after being rescued shortly before the alternate history disappears) follows them forward (but still long before his own time). He finds the villains (after a long time for them — so long they've forgotten everything except that he's the Enemy), but is unable to stop them; they travel back in time, and he's only saved by a time machine — allowing him to return to his own time — which he then sends back with the instructions for what he just did. Finally, he's told not to worry that he didn't stop the villains; they've just travelled to the first place he met them, where they will then travel back and create an alternate history where Napoleon conquered Britain, before...
The novel Q-Squared introduces several alternate realities, including one based on the Bad Future in Yesterday's Enterprise. However, in this case, when the Ent-D finds the Ent-C, all the crew aboard it are already dead. Afraid of Klingons getting their hands on a Federation warship (even an old one), they scuttle it and move on. Oh, and by the end of the novel, that reality is even worse off, since its Picard and Riker are dead.
The Star Trek: Department of Temporal Investigations series attempts to defy this trope by introducing a semi-consistent theory of temporal physics that can be used to explain the vagaries of time travel throughout the franchise. No small task, considering how haphazardly the subject has been handled over the years. While it does require a fair bit of Technobabble to get through it all, the result is remarkably coherent, with the added benefit of helping to justify the timey-wimey ball approach within the Star Trek Universe. Temporal physics are so complicated that even the Federation's best researchers don't fully understand it, which means we can't always take for granted that Starfleet laymen know what they're talking about when explaining how it works.
In A Tale of Time City by Diana Wynne Jones, the titular city exists outside of the flow of history on the rest of the world. From this vantage point, the citizens see that history works like weather patterns — it shifts back and forth with minute details thanks to the butterfly effect and time loops. Basically, a more detailed explanation of the Timey-Wimey Ball, where shifts in the time travel theories are explained away as the changing "weather patterns" of time. For instance, on one day in Time City the inhabitants may observe that World War II begins in 1939, but on another day they may notice that it has changed to 1938. Perhaps time in the book is two-dimensional, with Time City time orthogonal to time everywhere else. Except it turns out that the history of Time City can shift back and forth too...
In Jasper Fforde's Thursday Next novels, not only do the rules of Time Travel make no sense whatsoever, the main character (whose father is a time-traveller) realises this, and often lampshades it. In one book, the rules actually seem to change over the course of a conversation with her dad, but she realizes there's no point in even asking.
In First Among Sequels, there is a subplot revolving around the fact that the time-travellers have mapped almost the entire future and found that Time Travel has not yet been invented. By the end of the book, Thursday and co. have managed to ensure that Time Travel is never invented, and thus, could never have been used earlier in the series. This means that several events from the previous four books including the plays of William Shakespeareand the beginning of all life on earth logically could not have happened. Since many of these events were the results of Stable Time Loops anyway, this is a case of Ascended Time Paradox. Or Mind Screw turned Up to Eleven. Either way, it's probably best just to apply the MST3K Mantra and enjoy the series.
A significant part of the plot of The Woman Who Died a Lot is that the non-existence of time travel in a world where many people know they used to work for the ChronoGuard has actually made the Timey-Wimey Ball worse.
In We Can't Rewind, the narrator makes several attempts to make sense of how his world's peculiar form of time travel works for the readers, and then gives up, explaining that he'll probably lose his mind if he keeps this up for much longer. He mentions that the temporal theorists of Merciar, from which he's writing this account, are doing no better at settling their controversies over how exactly inter-dimensional time travel works, and that most of Merciar's citizens have already given up trying to make sense of it in order to preserve their sanity and advised everyone else to do the same.
In Connie Willis's stories, the time machine sends you not to your target time-and-place but to the nearest point such that your actions will not change history. (This is consistent with James Hogan's theory mentioned above, though the mechanism is not explicitly stated.) In Doomsday Book (which shared the Hugo Award in 1993), a history student aiming for England 1328 lands instead in 1348, where she can't affect history because everyone she meets will shortly be dead of the Plague.
World of Warcraft: The novel trilogy War of the Ancients. Despite some dramatic changes (such as saving an entire race that originally went extinct), it's apparently okay to mess with time as long as the end result is roughly the same. Of course, it also helps explaining why said race appears rather plentiful in World of Warcraft after having been said to be extinct in an earlier novel...
