Earth (or another species' homeworld) has fallen victim to some disaster and is no longer inhabitable. But fear not, we managed to get some people off before it was too late.
For some reason this seems to be the sole reason for interstellar colonization in most "mainstream" sci-fi.
Always results in a case of Earth That Was, though in some cases of that trope the space colonies existed before the disaster.
Dragon Ball Z: When the Namekian homeworld is set to explode by one of Freiza's attacks, a wish is made on the dragon balls to save their lives by evacuating all the Namekians to Earth.
The Authority do this in one arc, evacuating the planet's entire population so as to cause less collateral damage when fighting a superpowered villain.
WALL•E - Humanity relocates to ships like the Axiom for 700 years.
In Titan A.E., the alien Drej vaporize Earth in the opening sequence while refugee ships try to escape.
In Battle for Terra, Earth, Mars and Venus have all been blown up, so humans go to the eponymous planet to find a new home.
The movie Oblivion (the new one) has humanity attempting to escape a ruined Earth that has been wrecked during an Alien Invasion war, settling a new colony on Titan. Of course, this is a big damn lie, but saying any further details is a massive spoiler.
In the live-action Transformers film Cybertron was destroyed in the Autobot / Decepticon war and they search for the Allspark in order to rebuild it.
In Last and First Men the Fifth Men migrate to Venus when the Moon (destabilized millions of years earlier in the Martian/Second Men war) starts to crash into the Earth. And the eighth men design the ninth to colonize Neptune when the sun expands to cover the Inner System. But eventually the sun goes nova too quickly for the Eighteenth Men to devise a means of escaping to another system, though they do manage to send out "seeds" of life that might eventually evolve into new humans.
In the "The Homecoming Saga", a series of 5 novels by Orson Scott Card, the Earth was rendered uninhabitable by human wars, and mankind departed for Harmony, as well as at least forty other planets.
In Walter Jon Williams' Aristoi, Earth was destroyed by Grey Goo, leading to the reorganization of society into essentially a confederation of feudal states, with each state's leader (the Aristoi in question) being the only ones allowed to use nanotechnology freely.
Arthur C. Clarke's Rescue Party has aliens coming to Earth in order to try saving at least a few humans before the Sun goes nova. In the end, it turns out the humans built a fleet and left already.
Robert Sheckley has an amnesiac human waking up on a starship, apparently the last survivor after a nova. The ending reveals he serves as a Neuro-Vault for the entire humanity.
Gianni Rodary has two short stories about aliens from a threatened planet settling on Earth.
Isaac Asimov's The Currents of Space end with a planet (not Earth) being evacuated - its sun is about to go nova.
The premise of Space Mowgli is that Terrans intend to evacuate the Human Aliens of the planet Panta, whose sun is about to explode, to the planet Ark (named after Noah's Ark).
In Beetle in the Anthill, the scientists speculate that the entire population of Hope (the planet Abalkin explores in the flashbacks) was evacuated to another (unknown) planet by the Wanderers.
The Insects From Shaggai (AKA Shan) in Ramsey Campbell's Cthulhu Mythos stories. When their home planet was destroyed by a Mythos abomination, some of them fled to a succession of other planets, finally ending up on Earth.
In the backstory to the Gor series the Kurii destroyed their homeworld in intercine battles, so they went looking for a new home and found Earth & Gor. The Priest-Kings have waged a war against the Kurii to keep them out for millenia, all unseen by most humans.
In the Isaac Asimov book Robots and Empire which links his Robots series to the Foundation series, a robot causes/allows a radioactive explosion which will slowly poison Earth, forcing the population to expand out into space.
A surprisingly consistent point of future history in Doctor Who foretells the mass evacuation of Earth around the thirtieth century, to avoid solar flares. The Eleventh meets the Starship UK in "The Beast Below", but it comes up in other episodes as well. In addition the fourth Doctor encounters a wheel-type space station full of sleepers in The Ark In Space, which is set 20,000 years in the future implying that it happens more than once.
The National Geographic special Evacuation Earth has as its premise a wayward neutron star heading towards Earth and attempts to build a Generation Ship to take 250,000 people to Bernard's Star.
In Defiance the Votan Collective came to Earth when a supernova destroyed their home system.
On the Planet of the Week in the Stargate SG-1 episode "Lifeboat" SG-1 finds a crashed Sleeper Starship built by a human society called the Talthuns, who had evacuated as many people as possible before their planet was destroyed by a coronal mass ejection caused by a "dark star".
In the Babylon 5 episode "The Deconstruction of Falling Stars", which flashes forward to different eras of humanity's future after the show's time frame, it is shown that humans evacuate Earth one million years in the future, before an impending mysterious artificially-induced nova explosion of Sol.
Star Trek: The Original Series episode "The Empath". The star of the Minarva system is about to go nova. A group of highly advanced aliens known as the Vians can save the population of only one of the planets in the system. They decide to determine which planet's population will be saved by putting a member of each population through a Secret Test.
During The Fall in Eclipse Phase millions of people uploaded their Egos to the sparsely-populated colonies in other parts of the solar system (uploading being the easiest means of space travel), while some others crowded the Space Elevators and crammed aboard ships.
Classic Traveller, Double Adventure "The Chamax Plague/Horde". In the Back Story, the alien population of a planet was close to being wiped out by a Super-Persistent Predator species called the Chamax. They decided their only chance was to build a fleet of Sleeper Starships to carry all of the remaining aliens to other star systems.
BIONICLE: In the Kingdom Alternate Dimension, Matoro fails to revive the Great Spirit Mata Nui, leaving the Matoran Universe in danger and prompt mass exodus onto the island of Mata Nui. Not all beings made it safely, but while many made it to the island, it is only a temporary refuge. The survivors settled quickly and also planned on how to leave the island for the stars.
Homeworld: The Mothership was meant to be a colony ship before the Kushan even were aware of the threat to their existence, but when the Taiidan incinerated Kharak's atmosphere it became necessary to their survival as a species.
Earth, or Lost Jerusalem as it's called, is referred to often in Xenosaga. Humans had to leave it because of a mysterious space-time disturbance. Its location has been long lost. At the end of the third game a chunk of the party goes off searching for it, and we're left wanting another sequel.
The backstory for its spiritual prequel, Xenogears, is similar. Humans left Earth in AD 2510 due to a space-time anomaly. The only reference to Earth in the game, though, is in the intro, and it is called "the main planet."
In Outpost 2 the human race has fled from an asteroid-doomed Earth. The plot of the game revolves around the earthling colonists of a new planet and how they destroy themselves all over again.
Another non-Earth example: The D'ni of the Myst series originated on a world called Garternay, which became uninhabitable when its sun began growing dim. Their ancestors fled into a succession of other worlds via their linking books, and have since lost all contact with their abandoned homeworld.
In SimEarth, if the sapient civilization develops past the "nanotech age", an event called "the exodus" is triggered. All cities, regardless of tech level, are fitted with engines and take off into space. The planet is declared a preserve and left alone, possibly allowing a new sapient species to evolve. The motivation for the exodus is unclear.
In the RTS Earth2150, this is the ultimate goal of all three factions, on account of the imminent Earth-Shattering Kaboom. Throughout the campaigns, you not only have to complete missions to cripple your rivals, but stockpile your excess resources in order to build a colony ship to carry you to another world before the countdown expires.
This is a common last resort for species attempting to survive a Reaper invasion. Of particular note is a Side Quest to save the Elcor, whose homeworld is being assaulted, in Mass Effect 3. However, this only serves to delay the inevitable, because the Reapers are patient enough to spend centuries exterminating every last trace of all sapient life, no matter where they hide.
Before the story proper, the quarian race escaped their homeworld to avoid being exterminated by the robot race they created, the geth. Worthy of note is that the geth allowed them to leave to avoid committing genocide.
In Orion's Arm Old Earth suffered a Grey Goo outbreak known as the Nanodisaster, but that's not why it was evacuated. The outbreak was nullified by an AI named GAIA and e decided humans were the worst threat to Earth so e told us to leave, before e sicced eir nanoswarms on us. E was considerate enough to build a fleet of ships first though.
Five hats means that five tropers think it is ready to publish.
You are saying that you think this draft is ready to be published. That means the description is not ambiguous,
it doesn't duplicate an existing trope, there are at least three examples, and the title makes sense.
Is that what you meant to do?
You are saying this draft has a ready-to-publish hat it does not deserve and you are taking it back.