Often in SciFi, by the time humans are colonizing other worlds, Earth is united under a single government (often a United Nations that’s suspiciously US-like, but I digress).
One novel series that bucked the trend (spoiler alert for an old Harry Turtledove series) is the Worldwar series, where Earth is invaded by aliens in the midst of World War 2; they manage to conquer much of the world, but the five biggest players in WW2 - both Allies and Axis - manage to remain independent by reverse engineering alien tech and eventually developing nuclear weapons.
In the later books in the series, there is a space race (mostly in the background/between books) where both America and Germany visit Mars, and eventually the US develops interstellar travel and (at the very end of the last book) FTL; it’s implied that Japan is about to develop FTL too.
That’s where the series ends, which is a shame, because the idea of a bunch of interstellar empires who all have their capital on the same home planet where they all originate sounds fascinating. Which leads me to my question: are there any other SciFi books or other stories that explore this concept?
Along those lines, We Are Legion (We Are Bob), deals with multiple superstates attempting extrastellar exploration via Von Neumann probes, where the protagonist is an AI version of a cryogenically frozen human. The former US is now a theocracy, Europe is basically a supersized EU, with China and Brazil taking over their respective continents, Africa banding together in one republic, and Australia’s just down there like “WTF, mate?”
The novel Gateway, by Fredrick Pohl, was about a alien artifact that could send ships to other solar systems at faster-than-light speeds. The artifact was controlled by a great power consortium of the United States, the Soviet Union, Brazil, New People’s Asia (which was an expanded China), and Venus.
All the ones you mention except Africa launch probes.
This was also the first thing I thought of when I read the OP; though the overall premise turns out quite differently than what I think the OP is looking for…
Fred Pohl’s Jem has independent expeditions from three multinational groups (food-producing nations led by the US, oil-producing nations (UK, Middle East +), and large-population nations (China and India)) landing on an extraterrestrial planet. It does not go well on Jem or on Earth.
Poul Anderson’s After Doomsday also has independent expeditions from Earth (an American one with a male crew and a European one with a female crew).
In Alastair Reynolds’ Chasm CIty, several nations each send a ship among a flotilla. The ships competing (to the point of violence) to be the first to arrive at the destination is a major plot point.
In the game Freelancer, there are a few factions that are basically holdovers from Earth nations: the US, Britain, Germany, and Japan. Spain too, but the ship malfunctioned.
Mass Effect does it halfway - Earth is still divided into dozens of sovereign nations, but on the interplanetary scale they have a common military and a digital currency which can be converted to and from one’s local currency on demand.
None of this ever actually comes up in the gameplay, though, as the only time you ever get to visit Earth is during an invasion of omnicidal robots.
Voyage From Yesteryear by James P. Hogan involves the arrival (after a world war) at Earth’s only colony of a starship from the USA’s successor state, with a starship from a competing superpower due to arrive in some years behind them.
A World of Difference by Harry Turtledove is set in an alternate universe where instead of Mars there is the larger life-bearing world of Minerva. The story is about competing expeditions from the USA and USSR to it (the USSR has lasted longer in that timeline).
Joe Haldeman’s Worlds has several earth-orbit colonies, though many of them seem to have been created by corporations or even churches, rather than Earth’s governments. On Earth, there are many different governments until a massive war breaks out near the end of the book and most of the population of earth dies or descends into anarchy.
The Moon Is A Harsh Mistress has a world government, the Federated Nations (FN), but individual nations thereof seem to have a great deal of autonomy - note that their actions independent of the FN of recognizing the Luna government are instrumental to the conclusion of the plot. Certainly the Lunar warrens of Novylen and Hong Kong Luna allude to being peopled largely by deportees from the Soviet Union and China, respectively
In the Hammer’s Slammers series by David Drake most of the first generation interstellar colonies were founded by individual Earth nations, though the current state of the Earth’s government is unknown - it’s mentioned in passing a few times but never visited in the series. Some planets, such as Nieuw Friesland, were founded by a consortium of corporations instead.
John Hemry’s JAG in Space series has competing Earth nations with a military presence in space (mostly relatively nearby Earth, but with outposts considerably further away). The novels are entertaining, involving a junior officer, who, because he’s assigned as ship’s legal officer (he had taken the one-semester course at the academy so there was no one more qualified), ends up involved in various legal issues affecting his ship and its officers (each one apparently inspired by a real event involving the US navy in the 1980s)
For All Mankind on Apple TV has a 7-member international alliance working on Mars in 2003. Individual countries included are the US, Soviet Union, Japan, North Korea and India. The other 2 members are the consortiums of the European Space Agency (covering most of Western Europe) and the Coalition of Communist Countries for Spaceflight (which includes most of the Eastern Block nations, but also Egypt, Greece, Turkey, Venezuela and Mexico).
Some of the individual countries that are part of the consortiums have their own national manned space programs.
The Hope Hubris series (Bio of a Space Tyrant) by Piers Anthony feature multiple nations in space. Much of the 1980’s era political landscape was represented there.
I enjoyed it as a teen, but have a lot less tolerance for sex with very young females today.
Ken MacLeod’s latest series, The Lightspeed Trilogy, starting with Beyond the Hallowed Sky and set mainly later this century, has the three major political power blocks on Earth all discovering FTL travel separately and keeping it secret from the general population. Their different secret space forces then jostle for control of habitable planets, etc.