Constructed World

"There are no children called Colin and Susan from our world who fall into it to become the main characters."

—Terry Pratchett, praising The Lord of the Rings

A Constructed World is a completely fictional setting, rather than our world in The Future, another planet in our galaxy, or an Alternate History. The heroes of its stories are usually the locals, who neither have nor need a connection with our present-day Earth.

This world might be built from standard components, but there is deliberate World Building going on.

As one of the most common fantasy settings, some form of Functional Magic is typically present, but this isn't required: constructed worlds exist that have little or no magic. Most High Fantasy takes place in constructed worlds, as well as a great deal of Low Fantasy and Heroic Fantasy.

See also Paracosm. Compare A Long Time Ago in a Galaxy Far Far Away, which is used more in science fiction but usually has the same effect. Contrast Magical Land, where the focus is on visitors to the setting. Earth All Along is a subversion of this trope.

Examples of Constructed World include:

Anime and Manga

Daikurikku in Simoun. In fact, figuring out its bizarre laws (and the meaning behind pseudo-Latin terms) is among the (many) fun points of the series.
The unnamed world of Eiichiro Oda's One Piece has very distinct geography and weather completely different from our Earth. And the Fantasy Kitchen Sink mythology and the Schizo-Tech, like the telecommunication snails ...
Similar to One Piece, Dragon Ball takes place an an Earth-like world that clearly has nothing to do with earth.
The setting of Royal Space Force: The Wings of Honnêamise is similar to Earth during the early Space Age—but not identical. Almost everything about the world, from geography to clothing to eating utensils, is at least slightly different.
One of the Fullmetal Alchemist canons is this. The other is not.
Naruto is set in an unnamed world on an unnamed continent (or maybe subcontinent), but is clearly fictional and a lot of World Building is done early on (for instance, we learn about the politics and geography of the world hundreds of chapters before it really becomes relevant). Being a series about Ninja, it has a lot of Japanese influences.
Windaria, at least in Streamline's English release, is completely unexplained.
Record of Lodoss War, and its spinoffs Legend of Crystania and Rune Soldier Louie.
Amon Saga.
Digimon X Evolution

Comic Books

Estarcion from Cerebus the Aardvark

Literature

J. R. R. Tolkien's Middle-earth is the Trope Codifier of this trope. His own term for this type of setting was Secondary World. Hilarious in Hindsight, since Middle Earth, also known as Midgard, is, in fact, our earth - only set in the far-gone mythical past of gods and monsters - specifically as a far, far prequel to all Anglo-Saxon myths.
The setting of The Wood Beyond the World. William Morris is usually credited as the creator of the modern "invented world" fantasy (departing from the tradition of setting fantasy stories in Arthurian Briton, fairyland or Arabian Nights-esque Arabia). Tolkien read the novel as a child, and it was a major influence on his work.
Terry Pratchett's Discworld has no physical connection to our own. However its basic nature is based on several old theories about how our world works, such as it being flat, and being orbited by the sun, and being on the back of a giant turtle. Its cities, nations and sometimes individual people are often clear analogies to those from earth's past and present.
- In the The Science of Discworld books, there is a connection between the Disc and Earth, but so far it's only been used for the wizards to visit our world, not for Earthers to visit theirs. Except once in the third book, and then it's by accident and they return Darwin to Roundworld ASAP.
Tarra in Arcia Chronicles.
Kertiana in Reflections of Eterna by the same author.
Terreille (the Realm of Light), Kaeleer (the Shadow Realm), and Hell (the Dark Realm) in Anne Bishop's Black Jewels series. They seem to bear no relation to our world, and the human races may not be human as we understand it.
In Michael Moorcock's The Elric Saga, Melniboné and the surrounding New Kingdoms. Like Middle Earth, it's supposed to be Earth's long-forgotten past, but is so different it may as well be another world.
The continent of Westeros and the rest of the surrounding world from George R. R. Martin's A Song of Ice and Fire series.
Greg Egan's Orthogonal series (starting with The Clockwork Rocket). Not only does it have no connection to our world, it doesn't even use the same laws of physics.
Brandon Sanderson's adult fantasy all takes place in the same verse called the Cosmere, Word of God has officially stated that Earth does not exist in the Cosmere.

Tabletop Games

Every Dungeons & Dragons campaign setting ever (except for Masque of the Red Death).
A lot of role-playing games. Listing them all here would break the article's back.
All of Magic the Gathering's planes are original; none of them are based on Earth, and it's generally considered canon that our universe is not part of the Magic multiverse.

Toys

The Bionicle universe had no connection whatsoever to ours, despite inter-dimensional travel being possible there. Multiple alternate universes and pocket dimensions exist, but none resembling ours. The creators have avoided having live-action adaptations of the series for fear that this segregation from the real world would be compromised in order to make way for a Human-Focused Adaptation.

Video Games

The Twin Worlds of The Longest Journey are somewhat of a gray area. On one hand, its starts off as your regular run-of-the-mill Cyberpunk dystopia. On the other hand, we soon learn, that what we perceived as "Earth" is actually a world called "Stark" and it has a twin world named Arcadia that does not follow the laws of science but instead is governed by chaotic magic. What's more, these two worlds are, in fact, Earth... or, at least, they were Earth twelve thousand years ago. Therefore, there is a connection called "Balance" between them which has its own eerie rules...
Strangereal, the original Ace Combat setting, is a completely independent world, despite being heavily based on modern-day Earth.
The Iron Grip series has Theia, a Planetary Romance Earth analogue with wildly anachronistic Punk Punk societies and nations, an ice age climate and a Purely Aesthetic Era feel.
The noir fantasy world of the Thief series (though it does have characters with Earth-like names, it's very clearly set in a setting completely removed from everyday reality).
The unnamed but obviously constructed world of the Drakan series.
Celenheim in Enclave.
Azeroth from the Warcraft series and World of Warcraft.
The Elder Scrolls is set in a very well-constructed world called Nirn, though the games are set primarily on a single continent called Tamriel.
Shining Force has its own fictional map.
RuneScape is set on the Medieval European Fantasy plane of Gielinor.
Arcanum: The eponymous Arcanum.
Diablo: Sanctuary.
Dragon Age: Thedas. Incidentally, even the name of the world is constructed: it was a shortcut for "The Dragon Age setting" used by the developers until they decided to Throw It In.
Dungeon Siege: Aranna.
Sacred: Ancaria.
Septerra Core: Septerra.
Siege of Avalon: Eurale.
The Legend of Zelda: Hyrule.
Super Mario Bros: The Mushroom Kingdom.
Star Fox: The Lylat System.
Almost all of the Final Fantasy series: Every game takes place in its own constructed world.
The Neverhood: Constructed out of clay.
Early western promotional materials for Sonic the Hedgehog. The games are now set on Earth.
Dark Souls: Lordran.

Web Comics

Overside, the setting of Rice Boy, Order of Tales, and Vattu.
Archipelago though it might just be in the future.

Web Original

Neopets takes place in a world called Neopia. It has Bubbly Clouds; a floating Mordor; Two medieval worlds; a pirate island; a tropical island with Mayincatec ruins in the jungle; Ancient Grome; Wutai; an icy mountain; A haunted forest with a Circus of Fear and Überwald; A Steampunk city/Lethal Lava Land; An Egyptian desert; an underwater city that rose from the ashes of Underwater Ruins; Prehistoria; A space station; a moon; and a ~~world made of jelly~~ that's just silly. Schizo-Tech doesn't begin to cover it.
Guts and Sass: An Anti-Epic draws inspiration from various low-tech Earth cultures, but has a distinct set of original semi-domesticated pastoralist, feudal agriculturalist, Proud Warrior Race, merchant-trader, and hunter-gatherer cultures. It also features original landmasses and ocean currents, as well as an alternate tidal catalyst (the planet has no visible moon).
RWBY: The world of Remnant, with its oversized, shattered moon, its unfamiliar continents, Mana in mineral form, and active Physical Gods in its ancient past, is clearly no version of Earth.
Dofus and Wakfu take place in the World of Twelve, a planet located on its own solar system, in a universe called the Krosmoz. On this planet, there is the continent of Amakna, and also a few islands scattered throughout, like Pandala, where the followers of Pandawa live, and a small island where the alchemist Otomai lives. In the timeline of Wakfu, the world suffered a terrible flood, with half of it being submerged, in an event known as "Ogrest's Chaos". After this, the continent was no more, and the four cities of Amakna became separate islands.

Western Animation

Avatar: The Last Airbender. While it certainly has elements of various Asian and First Nation cultures, its certainly a very separate fantasy world.
Epileptic Trees about it being Earth After the End notwithstanding, Equestria from My Little Pony: Friendship Is Magic is a world all its own and differs from our reality in several significant ways (such as the fact that all forces of nature are controlled by magic ponies).
In the 2011 ThunderCats reboot, though it has an Alien Sky and the name "Third Earth," the planet the eponymous Thundercats inhabit is a lunatic Heroic Fantasy Kitchen Sink, with Petting Zoo People, magic swords, Sorcerous Overlords, fruit made of candy and Schizo-Tech.