Were I to continue this process of identifying those books that make up the Heart & Soul of 20th Century science fiction with another 10 books, this is what I would recommend:
1) Do Androids Dream of Electric Sheep? by Philip K. Dick
2) The Einstein Intersection by Samuel R. Delany
3) On Wings of Song by Thomas Disch
4) Nineteen Eighty-four by George Orwell
5) The Dragonriders of Pern trilogy by Anne McCaffrey
6) The Space Merchants by Frederick Pohl & C.M. Kornbluth
7) The End of Eternity by Isaac Asimov
8) The City and the Stars by Arthur C. Clarke
9) The Beast that Shouted Love at the Heart of the World by Harlan Ellison
10) The Past Through Tomorrow by Robert A. Heinlein
Here again we see the importance of the short story with two more titles, and find one of the single-author collections is by Heinlein. His influence on science fiction in the 20th Century is probably (and arguably) greater than any other single author. He has written classics in the genre of all types, from adult novels to juveniles, from short stories to novellas. Starship Troopers begat the subgenre of "military SF" while his juveniles impressed themselves upon scores of teenagers who would some day turn to writing themselves. Yes, at times his stuff reads like Libertarian wish fulfillment (but that’s only because, at times, it was). For all that, his collection contains some of the best short stories seen in science fiction.
Asimov and Clarke each have a book in this grouping as well, further underlining their prominence in the genre as, with Heinlein, the triumvirate of science fiction, and their influence in shaping the heart & soul of SF. While Heinlein may have had the greater influence on the genre, Isaac Asimov was probably the true soul of the genre. Indeed, personally, my love of science fiction took root with Heinlein, grew into Asimov and then matured with Clarke (and Bradbury, who always stood apart from the other three in my mind as coming at SF from a literary/artistic place as opposed to an idea-centric place.
The City and the Stars is a great example of Clarke’s continued success in evoking a “sense of wonder” while still managing to tell a wonder-filled tale. The End of Eternity is one of Asimov’s most sophisticated and rewarding novels, truly an example of his growth as a writer from the Foundation days.
Nineteen Eighty-four is a classic in literature as well as in the genre. It is the ultimate dystopian novel. It is also one of those SF books that affected our culture at large by giving us the phrase, as well as the concept of, “Big Brother.” This book may also be the main reason why “politcally correct” speech never really fully took root.
Androids may not be Dick’s best novel but as the source material for the movie Blade Runner it helped define the look and feel of cyberpunk later on, and perfectly represents Dick’s primary themes: what it means to be human, and paranoia. It is definitely another modern classic.
And, again, we have a collection of stories by Harlan Ellison who, to me, has become the poster-Infante of the science fiction short story. This collection includes "A Boy and His Dog," which won the Nebula award, and "Along the Scenic Route," and the title story, "The Beast that Shouted Love at the Heart of the World" won the Hugo award.
The Einstein Intersection is book that expands the boundaries of science fiction and speaks to the genres openness to experimental forms as well as "out there" ideas.
On Wings of Song injects the counterculture firmly into the genre and continues the tradition of commentary on society that runs throughout science fiction.
The Space Merchants looks at the ultimate sociological implications of advertising on society; it also tackles popular science fiction themes of runaway population growth and diminishing resources. Given the recent announcements of "lab grown meat" soon to become available, this novel may prove prescient in that regard (if I recall there was something about artificially grown chicken).
Finally, The Dragonriders of Pern trilogy would seem, by its title and the cover art of the edition I read, to be a work of fantasy, but it is definitely science fiction and the original trilogy spawned a whole series as well as an entire subgroup of science fiction fandom. Pern is a fully realized, well thought-out alien world colonized by humans and touches on the themes of utopia and genetic engineering (the creation of the dragons to protect humans).