Traveling Landmass

A landmass (usually an island) that is always on the move, making it difficult to find. Because of this, it's thought to not exist by most people, until one of the main characters finds it.

Examples of Traveling Landmass include:

Anime and Manga

The Shimaru homeland in Futaba Kun Change, which floats around because it is really a crashed spaceship that let the moss grow on the hull a bit over the years

Comic Books

Professor Semo's island base in the Mexican Fantomas comic book series.
Marvel Comics has Krakoa, The Island that Walks Like a Man!!! And to a certain extent Spragg, the Living Hill.
Justice League International: Kooey Kooey Kooey isn't always on the move, but sometimes it decides to wander for a bit.

Film

Seastar Island from the Doctor Dolittle movie (the Rex Harrison one) as well as the books. Explained in the book as a freak volcanic bubble during island formation creating a huge air pocket to serve as a float. When the rock at the top of the volcano drops down it punches a hole in the bottom to fix the island in place.

Folklore and Mythology

Greek myth gives us the floating island of Delos, birthplace of Apollo and Artemis.

Literature

Quofum, a planet in the Humanx Commonwealth universe, has an annoying habit of not being there when one goes to look for it. It turns out that the entire planet is some kind of dimension-hopping starship.
In The Witches of Karres, the titular planet is one of these. The residents like it that way.
- The residents control where it goes. To be more precise, they're the reason it moves: they managed to create an FTL "drive" that's not only faster than anybody else's, but capable of scaling up to shift their entire planet across interstellar distances. Useful, when they figure out that some of the neighbors have gotten panicky and decided to attack.
The 51st state of Ar, or Hoqhoq as they prefer to be known, according to John Hodgman. It's inhabited by shapeshifting thunderbirds.
The island of Leshp from Discworld which is a giant pumice dome that gets filled up with gas, rises to the surface, floats around a bit, then sinks again every couple of hundred years after causing a war or two.

Live-Action TV

The Island from Lost is constantly moving, thanks to a strange pocket of mystical energy.

Video Games

Mirage Island from Pokémon Ruby and Sapphire/Emerald.
The island in Tales of Legendia, although it turned out to be an alien spaceship.
The "Chocobo's Air Garden" in Final Fantasy IX will hover over 1 of 6 random locations on the world map. Once you've been there, it's current location can be found on the player's map, but before that it's identifiable by the circular shadow on the ground beneath it (hard to spot if it's over water). Getting there the first time requires the player to dig up all 6 pieces of the map to the island (which is really just a series of clues to the locations it might be found) by playing the Chocobo Treasure Hunt Mini-game and leveling up the Chocobo's abilities so that it is able to fly AND the use of a Dead Pepper every time the player wants to return to the Garden.
- The Air Garden gets you access to last couple Chocobo treasure maps, the optional super-tough side boss Ozma (but not the ability to HIT it with attacks, that's a whole other side quest), and the most difficult but most rewarding area to play the treasure hunt minigame (helpful if one is trying to pick up some of the semi-unique rewards).
Though most remember Angel Island from the Sonic the Hedgehog series, the original Japanese manuals say that the (sea-bound) island of the first game also moved around.
Simultaneously expressed and averted by the Floating Island in Subnautica. The island genuinely floats, having no connection to the seabed below it and lifted by the buoyancy of the huge, ancient "floater" creatures adhering to its underside. Its aversion comes from the fact that it is absolutely motionless: it never moves from its established location on the world map; it doesn't even bob in the water. It is perhaps the most rock-solid floating object you will ever encounter.

Web Original

Lutari Island in Neopets.

Western Animation

Candied Island in The Marvelous Misadventures of Flapjack.
A Saturday morning cartoon called Noah's Island; a polar bear called Noah travels around the world on a floating volcanic island, picking up lost, ostracised and endangered animals and trying to get them to live in harmony. The Animals of Farthing Wood meets Noah's Ark on a mobile island!

Real Life

Truth in Television: Continental drift. It's just so slow only geologists notice.
The island of San Serriffe, from a famous April Fools' Day hoax.
Icebergs. Sometimes used as temporary islands.
Astrophysicists now suspect that there may be stray planets wandering around in interstellar space, which were pulled out of their orbits when another star passed near their own.