The Lion, The Witch and the Wardrobe is one example.
Rahxephon—in this anime, Tokyo Jupiter is 12 years behind the rest of the world
Any others?
Time flows at different rates in the two worlds in Stephen King’s **Dark Tower ** series.
How about “Contact”?
Jodie Foster spends what he thinks is a long time in another world, having a lengthy conversation with an alien who’s adopted the appearance of her father. But when she gets back to our world, she finds that no real time has passed.
I’m sure there’s no end of these. IIRC, it’s the case in the Stephen King/Peter Straub collaboration The Talisman, for instance.
There are a lot more instances in science fiction of different time passage due to Suspended Animation (Buck Rogers), relativistic time contraction (Time for the Stars, The Forever War), or different physical processes (Dragon’s Egg).
Well, for songs, there’s '39 by Queen, one of the few about time dilation.
The movie “Brigadoon” about a city doing some major time-shifting.
For my money, the most emotionally powerful story along these lines is “Marooned in Realtime” by Vernor Vinge.
Dhalgren, by Samuel Delany, is set in American city in an indeterminate year(presumably late 20th century) which has been cut off from the outside world by an unexplained event. The denizens of the city are themselves unaware of what year it actually is, and publish a newspaper where the month and year on the masthead change every day.
In Piers Anthony’s Xanth series, the magical land of Xanth appears in different places in the real world at different times, so while time (AFAIK) passes at the same rate inside Xanth as outside it, someone who entered Xanth in the 21st century thinking it was Florida might leave a week later and find himself in 15th century Europe.
–Cliffy
Stephen Donaldson’s Thomas Covenant series
There’s two episodes of “Star Trek: Voyager” with this premise.
In one of them, either Paris and Tuvok or Paris and Kim (I can’t remember which one) are stuck on a deserted world with some alien for a few months, yet only a few days pass for Voyager.
In the other episode, it’s a more extreme time shift. Voyager goes in orbit around a planet, and in just the few hours or days they are in orbit, the planet goes from stone age level to about 1950’s level, eventually sending a rocket ship to investigate Voyager, since they cold see it in orbit before recorded history, and could see what it actually was since about the industrial revolution period. Voyager became almost like a god to them, thus causing quite the conundrum concerning the prime directive.
In the Disney cartoon “Gargoyles”, several characters travel to Avalon, where for every day that passes in the real world, only one hour passes there. I have no idea if they made this up, or if it’s a part of the acual legends/stories about Avalon.
Before the series went down the toilet and started imitating a different movie every week, there was an episode of “Sliders” where the sliders land on an alternate Earth where time passes more slowly, so Quinn Mallory is actually able to see himself as a kid and be reunited with a kind teacher that he had a crush on.
The trope is much older than Voyager:
Theodore Sturgeon’s “Microcosmic God” from the 40s deals with this: A man sets up an artificial society that advances millions of years in a very short time.
The late Robert Sheckley also dealt with the same idea with his “Starting from Scratch” from 1970.
Other examples:
David I. Masson’s classic story “Traveler’s Rest” is about an existance where time goes at different speeds depending on the latitude.
The protagonist is sent home from the war at the pole to his home near the equator. After many years, he is called back to fight again, finding he’s only been gone for a few minutes.
James Tiptree, Jr.'s “Time Sharing Angel” doesn’t really have different time rates, but people do experience time differently: you fall into a coma for a portion of a year, depending on how many siblings you have. For instance, if you had two brothers, you’d only be concious 1/3rd of the year.
Tiptree also wrote another story (“Fault,” IIRC), in which criminals are punished by having them “slip” in time, so they fall behind everyone, first by fractions of seconds, and by larger and larger gaps. Thus they react to things several seconds – and eventually minutes and hours – after they happen.
David Brin’s The River of Time, where everyone starts experiencing faster or slower time rates.
The Amber books by Zelazny and the Castle Perilous books by DeChancie both involve many alternate worlds with different time rates.
Between the Strokes of Night by Charles Sheffield involves a whole civilization that lives at a much slower metabolic/perceptual speed than normal humans. Advantages : subjective FTL travel, longer life span ( subjective as well; there are physical benefits to the slowed state ), robots that produce what you want “magically”, since they move too fast for you to see.
That original Star Trek with the ultra-sped-up race; the one that tended to die from even minor wounds and wanted to freeze the Enterprise.
Any number of stories involving Faerie.
Cosm, where a universe is created and observed while billions of years pass inside it.
The Heechee books, and The Crystal Spheres both have ancient races who hide in black holes to slow down time.
The Girl, the Gold Watch and Everything had a watch that stopped time.
There was a story I don’t remember the title of, where a missionary’s ship ( shaped like a gigantic illuminated cross ) fell in a black hole. Since time slows as you approach a black hole, it never hits from our perspective; there is simply a cross glowing forever against a black hole.
Known Space stasis fields virtually stop time for those within; creatures billions of years old can be recovered without having noticed any time lag.
In the comic book Amethyst, Princess of Gemworld, time passes differently on Earth and Gemworld, so, the title character (Amy Winston on Earth, Princess Amethyst on the Gemworld) is a 13 year old girl on Earth, a 20 year old woman on Gemworld. One presumes it to be part of the mystical nature of Gemworld that she actually changes form when she moves between worlds. Especially since she changes to her adult form in one issue without going to Gemworld. The difference is also variable (as in Narnia), so in one issue, she spends a short time in Gemworld only to find a long time has passed on Earth.
In the Buffyverse time goes at different rates in different dimensions.
I’m not sure but I think it’s true for Aspin’s Myth (M.Y.T.H) series.
I know there are other examples.
Brian
It sounds like you’re looking for more than conventional time travel stories, so I’m not sure this fits the bill. But the book “The Time Traveler’s Wife” by Audrey Niffenegger is the most original take on the time travel theme I’ve read. Though this is usually the stuff of sci-fi, this story is a romance that just happens to involve a man who has a congenital affliction where he spontaneously and involuntarily travels backwards in time, and returns again after some indeterminate period.
He travels back and meets a little girl who he becomes friends with, and meets her frequently on his accidental travels. She grows up, and meets him in his real-time. Of course, it was his future self who had been traveling backwards to meet her so his real-time self doesn’t know her, but she knows everything there is to know about him when they meet in his real-time. He figured something like this was bound to happen. They end up getting married. That’s really just part of the story. It’s quite engaging.
And yet another episode featured a segment where time moved in the opposite direction. As the sliders kept moving backward in that reality’s time, they had to make sure that they did whatever was required to ensure that the events they had just experienced – which are that reality’s future, keep in mind – would take place. I believe that segment ended when they preserved the life of someone who was supposed to die and ripped a hole in the universe.
You mean like Billy Pilgrim? 
And, on that note, I’ll add Vonnegut’s Slaughterhouse Five.
Groundhog Day is like this. Bill Murray’s character actually is moving forward in time in the sense that he is fully aware of his past experinces (he manages to learn to play the piano, for example). But everyone else is experiencing the recurring day for the first time.
Or, pretty much any story about Faerie from the past few hundred years.