There is a whole sub genre of broadly mid-century (usually) British children's books which take a particularly dreamlike psycho-drama approach to time-travel. Perhaps time-slip is the better phrase. All the British examples received adaptations by the BBC.
A Traveller In Time by Alison Uttly
Tom's Midnight Garden by Philippa Pearce
Moondial by Helen Cresswell
Charlotte Sometimes by Penelope Farmer
The Children of Green Knowe and its sequels by Lucy Boston
The Root Cellar by Janet Lunn (Canadian)
The concept of travelling forward in time can be found in several ancient stories:
In the ancient Indian epic Mahabharata, King Revaita travels to heaven to meet the creator Brahma and is shocked to learn that many ages have passed when he returns to Earth.
The Jewish religious scripture, the Talmud, mentions Honi HaM'agelgoing to sleep for 70 years and waking up to a world where his grandchildren have become grandparents and where all his friends and family are deceased.
In the 8th-century Japanese tale of Urashima Taro. Urashima Taro is a young fisherman who visits an undersea palace and stays there for three days. After returning home to his village, he finds himself three hundred years in the future, where he is long forgotten, his house in ruins, and his family long dead.
The concept of travelling backward in time is relatively more recent. The idea was hinted at in Samuel Madden's Memoirs of the Twentieth Century (1733), and told more explicitly in Alexander Veltman's Predki Kalimerosa: Aleksandr Filippovich Makedonskii (1836).
In 1632, the 20th century town of Grantville, WV, is dumped into the middle of Europe, during the Thirty Years' War. Beyond that transportation back over three centuries, though, there is no more time travel.
In The Adventures of Stefón Rudel, Stefón gets his hands on two time travel devices known as Korrekturuhren ("correction clocks") and travels back in time with them.
In Aeon Legion: Labyrinth, time travel is easy enough to merit a Time Police force named the Aeon Legion. People time travel by moving into a dimension called the Edge of Time where all time overlaps. The Aeon Legion also uses time travel to recruit those lost to history like MIAs in various wars. The time travel itself seems to operate on Timey Wimey rules.
Alterien: The Alteriens travel through time quite easily by using 4-dimensional space.
"The Immortal Bard": Dr Welch calls it "temporal transference", and uses it to bring many different people to the present-day, such as Archimedes, Newton, Galileo, and William Shakespeare. The Bard stays around long enough to enroll in a course dedicated to analyzing Shakespeare's plays.
Pebble in the Sky: An accident with crude uranium sends Joseph Schwartz from 1957 AD to tens of thousands of years into the future.
"The Ugly Little Boy": Stasis, Incorporated is a business where a Time Machine is used to move objects and people in a very limited capacity. When they perform the Stasis One experiment with Timmie, that's the nearest to their present-day that they can reach. As their technology gets better, they prepare to replace the Neanderthal experiment with Project Middle Ages.
Astral Dawn: Caspian and the Keepers travel back through time to stop Nu-Ba and the Defilers from destroying his other selves.
The Book of Dragons: In Camouflage 2020, the main character's final exam at the magical academy he attends involves projecting him to the time of the Punic Wars.
Bruce Coville's Book of... Aliens II: The aliens in Fine or Superfine? appear to be capable of this, as they're able to abduct a child from the mid-nineteenth and late-twentieth centuries simultaneously.
A Christmas Carol: The holiday-hating, greedy and apathetic Ebenezer Scrooge is taken away by three ghosts to spectate his past, present, and future. Each being place in time visited situated around Christmas.
The Cornelius Chronicles: The various protagonists time-travel more or less constantly — in fact with Jerry it's damn near involuntary. Oswald Bastable is also subject to this kind of involuntary shifting between alternate histories.
Doomsday Book, among other books by Connie Willis, features time-traveling historians who visit the past via a "net".
Downtiming The Night Side only allows a person to "jump" inside the body and consciousness of a person. The catch is that their minds get blended together so that with every jump, the time traveler retains a portion of the mind of the person they jumped into. Repeated jumps can overwhelm the time traveler's mind creating a completely different person. The protagonist gets so confused by this that he eventually occupies the body of a woman, the same woman he had earlier slept with and had children by.
Dragonriders of Pern: The earlier books used the newly-(re)discovered time-traveling ability of the dragons for several plot points. After the Big One (Lessa bringing the lost Weyrs back thorugh time with her) time travel was relegated to a Save The Day plot device due to the detrimental effects of dragon-based time-slipping.
The Empirium Trilogy: The main solution to ending the Undying Empire for good is to kill its leader, Corien, before he could create it. In order to do this, Simon has Eliana go back to the Second Age and try to talk Rielle into finishing off Corien.
Flight: Zits time travels continuously by going into different bodies.
Forerunner Foray: Ziantha is twice mentally thrown into the past by the artifact, as a Grand Theft Me taking over bodies from that era. Temporal paradoxes are not dwelt upon; she's just looking for the twin of the artifact she has.
Franny K. Stein: The Fran That Time Forgot has Franny retool her Time Warp Dessert Plate so she could go back in time to the day she was born and change her Embarrassing Middle Name. Unfortunately for her, the new middle name she gives herself still ends up getting her laughed at, and her telling her infant self that there's nothing worse than being laughed at creates a Bad Future where her teenage self creates an army of elephant monsters to terrorize everyone.
In Gene Wolfe's "Free Live Free" is a character study of some down and outers in 1980s Chicago, but uses time travel to enable the otherwise unexplainable series of events that reveal the main characters. The time machine is left behind when a time travel occurs. The means by which jumpers to the future are able to get back (not taking the machine with them) is very poetically handled if you see technology from a poetic point of view; Miyazaki might like it. There is never more than one version of a person, so if you go back to a time in which you previously lived, the previous you disappears when the new you arrives (but the travelling version is also affected by this by a folding in of character traits). This whole entry would be a spoiler on any other page, as the book is partly a mystery novel, and figuring out that time travel was involved is part of the detective's task.
Kim Stanley Robinson's "Galileo's Dream" ties together quantum mechanics and cosmology in its unique form of time travel, which manages to merge the concepts of Alternate Universe and Temporal Mutability — The Butterfly of Doom lives comfortably alongside You Can't Fight Fate. The book allows itself the leeway to be fantastical by basing itself in Renaissance fantasy literature, but it still manages to achieve this Timey-Wimey Ball in a very scientifically satisfying way. In fact, nearly every single time travel related trope manages to make an appearance in the novel in one form or another, with the plot turning out to revolve around a bona fide temporal war — a concept that is rarely made to make sense. Interestingly, in Robinson's universe, time is not a dimension — instead it is a manifold of three different dimensions, one of which conveniently runs backwards.
In Groom of the Tyrannosaur Queen a bit of sideways slewing in phase-space gets our the heroes to a lost time-colony in the Late Cretaceous.
Larry Niven's Hanville Svetz series of time travel short stories, collected in Flight of The Horse - where time travel is impossible in the real world, and every excursion that the protagonist makes is into a parallel, fantasy world that then directly affects his own. The reason for the jaunts? Well, the Secretary General of the UN in the series is a little mentally unstable (it has become a hereditary position, with serious inbreeding), and the protagonist is sent back in time to recover animals that the SG has seen in recovered children's books. You see, they don't exist in the heavily polluted future...to the extent that, in one story where the proliferation of cars did not take place due to time meddling, one of the supporting characters has to breathe exhaust fumes from a internal-combustion car to stay alive. Svetz finds a unicorn instead of a horse, Moby Dick instead of a sperm whale, a fire-breathing dragon instead of a gila monster... As is the case with most of Niven's work - it's all scientifically justifiable using the science known at the time of authorship.
In Harry Potter and the Prisoner of Azkaban, Hermione is revealed to have been using a time turner (which takes the form of a mini hourglass on a necklace) to attend extra classes. Harry and Hermione then go back a few hours in time to save Sirius Black from captivity. She gives back her time turner after deciding to drop two subjects. In Harry Potter and the Order of the Phoenix, Neville accidentally destroys the Ministry of Magic's entire supply of time turners, ensuring that time travel cannot play any further role in the story.
The Hitchhiker's Guide to the Galaxy explains that there can't be any temporal paradoxes, because "all the important changes have already been made."
On the other hand it also mentions that because of impatient building contractors with time machines, the great Cathedral of Chalesm was replaced by another building before it was ever built, thus making any pictures of it very, very valuable, blank, or both.
In The Restaurant at the End of the Universe, Marvin the Paranoid Android is abandoned for most of the lifespan of the universe due to time travel. It is later stated that, due to his various time travel incidents, Marvin is several times older than the Universe itself.
Household Gods: Nicole, a modern woman, is sent back in time into the 2nd century Roman Empire as a result of her foolhardy wish.
The Licanius Trilogy notably merges elements of High Fantasy with Time Travel. Certain characters have the ability to travel back into the past, though the general result is that the changes are deterministic and have already happened.
The Stephen Leacock story "The Man in the Asbestos Suit" treats the whole issue of time travel with complete flippancy, accomplished by eating too much junk food (a pork pie and a bag of doughnuts) and reading the London Weekly World News.
In Sean Ferrill's The Man in the Empty Suit, the narrator celebrates his subjective birthday every year by visiting a party 100 years after he was born. This, of course, means that every other version of himself is also in attendance. Temporal paradoxes are dealt with in an interesting way — each version of himself is "tethered" to a younger version. When one of them creates a paradox, they become "untethered", having come from different timelines, but still existing on the same timeline. Confused? So is he.
The Man Who Awoke by Laurence Manning has a rich New Yorker of 1935 create an underground vault shielded from cosmic rays and drugs himself into a coma. A timer activates an X-Ray tube thousands of years later to revive him. (Not implausible by the popular science of the 1930s.) Notable for suggesting the people of the future would revile our age for wasting natural resources. Also, one future age is dominated by virtual reality, another by a Master Computer, another by Anarchy Is Chaos.
In Poul Anderson's "The Man Who Came Early", an American soldier stationed in Iceland is sent back to the Viking Era after being hit by lightning.
Clifford Simak's novel Mastodonia manages to avoid all of the basic time-travel plots listed on the trope main page by having the protagonists travel only to the (relatively) distant past: fifty thousand years, seventy million years, twenty-five million years... There is a hint that the "Butterfly Effect" is a potential problem, but only if humans from the present encounter humans in the past.
In Gery Greer and Bob Ruddick's Max and Me and the Time Machine and Max and Me and the Wild West a time machine that one of the juvenile protagonists bought at a garage sale sends them into the bodies of people from the past for a limited time.
The novelization of the Merlin (1998) series implies that Lancelot came from a place in the future, or in a possible future, and was brought from it to the time of Arthur, by Merlin, to act as the king's champion. When Merlin first arrives there, they seem to have heard of him, though they never bring up what the history of their land says about it all.
One of the titular Midnight's Children has this power, though they don't seem to be able to actually affect events, only observe. They try to warn the other midnight children of impending doom, but they aren't believed.
In Millennium (1983) — and the film of the same name — the world is badly contaminated, so the government sends people to go backward in time, capturing everyone who was on a transport (plane, train, or ship) where all of the people on the transport were killed, or an event (a war, an attack, an explosion) where everyone in the area dies, and replacing them with cloned dead bodies so as not to change history. The problem is that once anyone goes to a particular time, no one can ever go back to anywhere during that period, the time period — an hour, two hours, whatever — is blacked out and unreachable. Visit a plane flying over the Atlantic Ocean for an hour and you can't go to Paris, New York or Antarctica at the same time later on.
Time-travel is essential to Mindwarp, a series that visits the distant future, the 1940s, and the prehistoric era.
Operation Do-Over: A car crash sends Mason Rolle's consciousness back in time to when he was twelve.
In the novel Rant, Rant uses a form of time travel to become his own stepfather.
Toward the end of The Secrets of the Immortal Nicholas Flamel, the conflict becomes less about stopping bad things from happening in the present and more about traveling to the past and ensuring that things happen the way they did.
In Septimus Heap, Septimus is kidnapped to 500 years ago, to serve as the Alchemist Marcellus's apprentice. He writes back to the future, and his siblings Jenna and Nicko, with their new friend Snorri, travel back to rescue him (though they arrive almost six months later than him). At the end of that book, Snorri and Nicko are still trapped in the past, and the next book is about Septimus and Jenna heading to the House of Foryx to bring them back to their proper time.
A Tale of Time City by Diana Wynne Jones. Time City is "outside" normal time, using recycled time (hence very important/emotional moments get burned in and are seen as time ghosts both before and after the event). Time is divided into unstable eras to be visited with great caution (ours obviously) and stable eras that they trade information with. However, they only sell information about the (relative) past, no stock market sneak previews.
In Tempest: A Novel the main super power so far is the ability to time travel. In the beginning, the time travel works more like an inverse of Ripple-Effect-Proof Memory where the main character goes back in time to an alternate past, but cannot change anything in the present. Actually time travel comes up but it involves Alternate Timelines and other complicated rules which have yet to be fully explained.
The Thursday Next series features multiple versions of history within a single book, but only the reader and the (off-screen) timetravelers are aware of this fact.
Time and Again, and its sequel From Time to Time by Jack Finney.
The Time Machine inspired 99% of the modern uses of the concept. The book used it to provide a present day frame story for a tour of the future.
The Time Scout series is built around an Accident that caused time portals to open up between random times and places. The stories cluster around people who happen to go places for various reasons.
The sequel, The Time Ships builds on the original, revealing what happens after the conclusion of the The Time Machine.
Time Warp Trio has its protagonists time travel through the "use" of The Book, a magical artifact that can send its wielder to any time period of its choosing. Oftentimes, the boys need to find The Book in the time period they landed in so that they can return home in one piece, and the story features time travel to the past and to the future.
Stephen Baxter's the Xeelee Sequence is THE quintessential Hard Sci-Fi Time Travel epic. It boasts one of the most realistic and comprehensive time travel stories ever written. In the Sequence, every FTL vehicle is a time machine. This is because under Einstein's general relativity, going faster than light breaks down causality. As such, the mechanics of time travel is not only thoroughly explained in the books, but it is also militarized on a tactical and strategic level. Characters or races from various books often time-travel back in time in a Stable Time Loop to achieve strategic foreknowledge. Any attempts to alter a faction's potential future to its advantage merely creates an alternate reality, which in turn, creates an infinite branch of temporal information that can be monitored by supercomputers that sends these signals backwards or forwards in time. And since each book of the Sequence is its own self-contained story whilst acknowledging the physics behind it, the Sequence avoids the many narrative pitfalls that plagues time travel-heavy stories such as paradoxes and plotholes. There is a reason why the Sequence is this sub-page's main image.
going to sleep for 70 years and waking up to a world where his grandchildren have become grandparents and where all his friends and family are deceased.