2001: A Space Odyssey (1968): A interesting case since the novel is actually the byproduct to a collaboration between Clarke and Stanley Kubrick, which resulted in the film of the same name that came out the same year, which makes the book the Novelization (Clarke himself said the book should have been credited to "Clarke and Kubrick", just like the movie was credited to "Kubrick and Clarke"). The book and the film are both based on some of Clarke's earlier short stories, most prominently The Sentinel, and they largely follows the same plot, but with some small differences.
A strange Monolith is discovered on the moon, apparently having been left there by a race of extra-terrestrial lifeforms. As it is being studied by human scientists, it sends some kind of transmission into outer space. About a year later a crew of five astronauts leaves for a scientific exploration travel to Saturn on the space-ship Discovery. Only two of them, David "Dave" Bowman and Francis "Frank" Poole, are left awake to help the sixth crew member, a supercomputer by the name of HAL 9000, with monitoring the ship's day-to-day function. This is just boring routine, until HAL starts acting weird and unpredictable, not only jeopardizing the mission, but also the life of the crew.
2010: Odyssey Two (1982): While not initially thought up by Clarke as a movie idea, the book was, in 1984, adapted, with his and Kubrick's blessing, into the film 2010: The Year We Make Contact.
Nine years after the Discovery's travel to Jupiter (changed from Saturn to match the film), a joint Soviet-American crew is heading for the mighty gas-planet to find out what happened to the Discovery and its crew. Meanwhile David Bowman, now reborn as a Energy Being, is helping the race that created the Monoliths with scouting Jupiter and its moons for primitive lifeforms, hopefully finding one that has potential to turn sentient.
2061: Odyssey Three (1987): Heywood Floyd, one of the main characters from the previous novels, has been invited as a celebrity guest for the spaceliner Universe's landing on Halley's Comet. Meanwhile a militant anti-Afrikaner takes control of the shuttle Galaxy, which she crashes into Jupiter's moon, Europa, leaving Universe as the crew of the Galaxy's only hope of rescue.
3001: The Final Odyssey (1997): The Discovery crew member, Frank Poole, having been killed by HAL 9000 and left adrift in space for a thousand years, is brought back to life through the wonders of future science, and begins to explore the earth of 3001. Meanwhile, the creators of the Monoliths are making their final speculation about whether or not to sacrifice human kind for the greater good.
This series of novels contain examples of:
Adam and Eve Plot: Marvel Comics' 2001: A Space Odyssey issue 7 has a Star Child taking two lovers from their doomed planet to repopulate on another.
Artistic License - Biology: Nicely averted when an alien life form eats a human, and then vomits it back up, pointing out that alien predators wouldn't necessarily find us tasty or nutritious.
Circumcision Angst: Inverted. A woman loses interest in Frank because his is circumcised, something that isn't done in 3001.
Everything's Better with Dinosaurs: In 3001, humans are able to clone raptors who are used for labor, and excellent babysitters. They tried using great apes (like gorillas), but as Frank learned, the apes "don't have the patience for it".
Faster-Than-Light Travel: Averted. Despite all of the monolith's powers, light speed is as fast as they can send information around.
Halfway Plot Switch: 3001 Is about a man brought back to life 1000 years in the future and Clarke's thoughts on what it will be like, then only the last third returns to the ongoing plot of the series.
Just Friends: Poole's relationship and eventual marriage with Indra is a form of this. They even managed to stay friends after the split up romantically 15 years later.
Living Gasbag: 2010: The Year We Make Contact had the noncorporeal Bowman journeying down through the Jovian atmosphere, where he sees gigantic non-sentient living beings in various geometric shapes floating through the clouds and consuming similar smaller creatures.
Nightmare Fuel: In-Universe in 3001, the people were terrified when they observe a planet explode, which triggered a supernova. They are left to wonder if there was intelligence on that planet or if they somehow caused it.
Oh My Gods!: In place of "God", the people of 3001 say "Deus", example: "By Deus - It's full of stars!".
Out of Focus: The Monolith appears in all but the final issue (#10) in the Marvel Comics' 2001: A Space Odyssey series.
Outgrown Such Silly Superstitions: By the year 3001, religion is abolished. That said, they aren't entirely disbelievers: they are generally either "Deists", believing in not more than one god, or "Theists", believing in not less than one god. What this God (or possibly gods) has to say about anything is eminently unclear, however.
Precursors: The mysterious race only know as "The creators of the Monoliths". The prologue gave them the name "Firstborn", but was never used in-story.
Sudden Sequel Death Syndrome: 2061 mentions that Dr. Chandra died in hibernation on the trip back to Earth after 2010. It's implied that he died of grief over HAL having been destroyed by the explosion of Jupiter.
Terraform: 2061 and 3001 depicts humankind as being capable of this.