Planet Terra

This is a fairly simple trope. It is simply the habit of calling Earth "Terra" in Sci Fi. The word is adopted from the Latin word for, well, earth. The advantages to doing this are simply coolness, especially when describing a human from Earth. Or just humans in general, in works that insist on naming species by their homeworlds. Terran just sounds more exotic and less condescending than "Earthling". Another advantage is that it is language-neutral, since it is by far the most common word for the planet—about six languages, give or take, call this planet Terra, while Earth, on the other hand, is purely English.

Calling Earth "Terra" may be a result of an Earth-That-Was scenario.

Anime and Manga

 * In Trinity Blood, Methuselahs refer to humans as Terrans. Because, as the original novels reveal,.
 * Toward the Terra.
 * In Outlaw Star, humans are mostly referred to as just that, but some characters refer to them as Terrans. Notably Aisha, and usually with a note of derision.

Film

 * In the book of the film for Men in Black, humans are called "terries". (At least by Edgar the bug, so it's likely a derogatory derivative of "terran".)

Literature

 * The government in Starship Troopers by Robert A. Heinlein is the Terran Federation.
 * The titular organization in the Terran Trade Authority series by Stewart Cowley.
 * The Saga of the Seven Suns series has the Terran Hanseatic League.
 * Most of Andre Norton's science fiction stories.
 * In Star Guard, an alien addressing the Terran mercenaries as "War Lords of Terra" pronounced it more like "Terror." He was worried that they might slaughter the people of his village, so "terror" was unintentionally appropriate.
 * E. E. "Doc" Smith's stories referred to our planet as both Earth and Terra. He also used the alternate name Tellus.
 * Poul Anderson's Technic History: The Dominic Flandry stories refer to Terra and the Terran (or sometimes Terrestrial) Empire.
 * An odd inversion is that Edmond Hamilton's Starwolf trilogy always speaks of humans as Earthmen, but the back-cover blurb describes the main character as a Terran.
 * Keith Laumer's Retief stories frequently use the abbreviated "Terry" for Terrestrial. There's no sense of it being derogatory, as the Terries use it themselves often enough.
 * In Sergey Lukyanenko's Line of Delirium trilogy, Earth is renamed Terra and serves as the capital of the Human Empire.
 * "Terra" and "Terrans" are used throughout H. Beam Piper's "Terro-Human Future History".
 * "Terra" is the most common name for the home planet of Perry Rhodan.
 * Earth has become known as "Terra" in S.L. Viehl's Stardoc series.
 * In Elliot S. Maggin's Superman novel Last Son of Krypton, Lex Luthor complains when aliens call him an Earthling, because he prefers "Terran". They explain that the translator operates according to the listener's intention, so if Luthor decides he wants to hear "Terran" instead, that's what he'll hear. (It works, at which point he decides to make the translations of his interrogators' names and species terms as insulting to them as possible.)

Live Action TV

 * The Star Trek Mirror Universe has the Terran Empire (until it collapses, at least). The main universe occasionally also refers to our solar system as the Terran System (though it's more frequently known as the Sol system or Sector 001).
 * Spock was asked in one Original Series episode if he was "Terran or Vulcan."
 * Blakes Seven  has a Terran Federation.
 * In Stargate SG-1 it was mentioned once that the Ancients called earth Terra, of course, Latin is derived from their language.
 * Though most of the time the Goa'uld word, Tau'ri, is used for humans from earth.
 * "Tau'ri" (lit. "The First World") is the name for Earth itself. Humans from Earth were originally referred to as "Humans of the Tau'ri," and was eventually shortened to just "Tau-ri" for the sake of brevity.
 * Played with and finally averted in the original Battlestar Galactica -- "Terra" turns out not to be Earth, but rather a splinter group from the Thirteenth Tribe that colonized Earth.

Tabletop Games

 * The BattleTech universe has the Terran Hegemony.
 * Renegade Legion has an imperial government known as the Terran Overlord Government.
 * Holy Terra is the homeworld of the Imperium of Man in the Warhammer 40,000 universe.
 * The Starfire universe has the Terran Federation.
 * The Terran Confederation in Traveller
 * Terrans are alternately called "Solomani"(men from the sun) and that is the preferred rendering in the Third Imperium era which is the default time of the GURPS line.
 * Inverted in Manhunter, the long out-of-print sourcebook for Rifts (and the only officially-sanctioned Rifts book not published by Palladium Books). The book has Earth as well as Terra, the later is a new homeworld founded by Humans after Earth was rendered nearly uninhabitable.

Video Games

 * In X3: Terran Conflict, the humans in the Sol system are referred to as "Terrans", but the planet is still called Earth.
 * The Galactic Terran Aliance from Free Space. Earth is still Earth, however.
 * In the sequel, two sides use Terran in their name: the Galactic Terran-Vasudan Alliance (composed of humans and Vasudans) and the Neo-Terran Front (composed of anti-Vasudan human radicals, with a vision of 'Neo-Terra' as an utopia for humans).
 * In StarCraft, humans are called Terrans, but strangely, the planet is still called Earth every single time it's mentioned.
 * And they're referred to as humans instead of terrans reasonably often.
 * Starcraft is actually a weird case of this, as the terrans are the humans not associated with earth. The people from earth still call themselves humans.
 * Wing Commander has the Terran Confederation, with "Terrans" occasionally being used by non-human races to refer to the speciess originating from Sol III.
 * In the Unrealverse, the Skaarj call humans Terrans.
 * PlanetSide has the Terran Republic.
 * The main race in the sequel to Galactic Civilizations is the Terran Alliance.
 * Rock 'n Roll Racing refers to Snake Sanders' home planet (very blatantly Earth-like) as Terra.
 * In Final Fantasy the setting is usually called "Gaia" (Greek for Earth) but in Final Fantasy IX the plot's impetus is an invasion by another planet known as Terra.
 * The Battle Opera Gunmech universe has the Terran Alliance.
 * Adventure Quest.
 * Used in the Crash Bandicoot series. Earth and Terra are separate planets, and one of the inhabitants of Terra believes Earth to be a copy of it.
 * In Mass Effect, the Star of Terra is one of the Systems Alliance's highest military decorations.

Western Animation

 * Battle for Terra is a subversion. Terra here is an alien planet named so by the humans fleeing the destroyed Earth. Its real name is unknown.

Web Original

 * All beings that can trace their lineage back to Earth in Orion's Arm are referred to as 'Terragen', and the region of space they inhabit is, obviously, called the Terragen Sphere. Note that most terragens were not actually born/created on Earth, and are hence not Terrans proper - they're just all, ultimately, descended from or created by Terrans.