Perhaps the best single story in the series is the first story in 2001 - life & times of primitive apes on the verge of discovering stuff that will make their descendants humans.
Second & third stories in 2001 hold attention. Former is a mystery; later is a space voyage.
3001, near its middle, has an interesting but somewhat philosophical discourse on human nature & the nature of our gods. I have included some quotes in the review of the book. And this discourse is essentially the same as that found about the middle of a much earlier novel - "The City & the Stars".
Rest of the series is of rather mundane quality.
Related other stories from Clarke.
- "The Sentinel": A precursor that was expanded in second story of 2001.
- "Transience": First part of this story deals with a period of human history similar in spirit to first story in 2001. But this is generally a different story.
- "Encounter at Down": A theme very similar to first story in 2001.
- "History Lesson": Features superfast evolution of life on a world newly made inhabitable, in a way similar to that of 2010.
- In the control room of the alien ship in "Rescue Party", there is a black rectangular screen that gives the impression of essentially infinite depth. It reminded me of monoliths that appear in various Space Odyssey novels.
- Essentially benign aliens keeping a watch on the development of intelligent beings everywhere in galaxy also appears in "Rescue Party". But in "Rescue Party", they physically visit each world once every million years.
- Anti-gravity devices that power the human spaceships in 3001 debut in much older "Rescue Party". There, the aliens use them to explore earth after they get off their ship.
- In some of the Odyssey sequels, you find tree like life forms on Europa that can move around. You also find a similar creature in a much earlier novel - "The City & the Stars".
Stories in this series unfold at many different locations in solar system: manned space habitats, Moon, Hally's Comet, Saturn, Japitus (a moon of Saturn), Jupiter, Io (a moon of Jupiter), Europa (a moon of Jupiter), Ganymede (a moon of Jupiter), & near a comet in Kuiper belt (beyond Pluto).
In each case, there are graphic & imaginative descriptions of the locale. They are generally good-faith descriptions of a fiction writer, & are sometimes dated. Consult some more appropriate source if you want accuracy.
Stuff borrowed from elsewhere.
Simulations-that-are-ghosts in later half of 2061 are very similar to simulations of two historical European figures that appear in at least 2 of the many sequels to Asimov's Foundation Trilogy (I don't recall the names of books but their story location is on Trantor, a hypothetical world that figures in many Asimov books).
Braincaps of 2061 follow very similar learning gadgets in one of the old Asimov stories (I don't recall the name of story).
HAL, the computer in 2001 & 2010, is a lot like robots in many Asimov stories. Difference is: Asimov's robots tend to be benign; HAL is not. But I recall at least one story by Asimov where robot becomes lethal in a pathological case somewhat similar to HAL; this story is set on planet Mercury & extreme heat affects the robot; I do not recall the name of the story.
Energy beings of 2001, & the way they transform the human Dave into a star child, are very similar to concepts of brahm & moksha in Hinduism.
2061 & 3001 liberally borrow passages from previous books in the series.