The Moon is Harsh Mistress, by Robert Heinlein
This 1967 Hugo Award winner coined the phrase, "There ain't no such thing as a free lunch," which has a special resonance in this story about a loose society of convicts and malcontents exiled in underground lunar colonies in the year 2075.
Ender's Game, by Orson Scott Card
Mankind itself is imperiled (something of a theme in the Sci-Fi genre) in this 1985 novel by Scott Card, who wrote the short story Ender's Game is based on while working at BYU Press. The games in this book are serious indeed, as Scott Ender must employ all the tactical brilliance at his command to defeat the Formics, an alien race of, well, giant ants.
Neuromancer, by William Gibson
One of the most popular books, in any genre, of the last 30 years, Neuromancer was the first winner of the Sci-Fi Triple Crown, taking the Nebula, the Hugo, and the Philip K. Dick Award after it was published in 1984. The book tells the story of a has-been hacker who comes out of retirement to perform the ultimate job. Bonus? Gibson regularly tweets at @GreatDismal.
Fahrenheit 451, by Ray Bradbury
As longtime bookies will recall, we quite nearly read the Bradbury classic in the very first edition of 1book140 (then called 1book1twitter). We're giving Fahrenheit 451 a second shot. Simply put, it's one of the most influential works of the 20th Century, the quintessential defense of literature in an anti-intellectual, book-burning epoch (pick your dystopia, past, present, or future).
Journey to the Center of the Earth, by Jules Verne
What would any list of classic science fiction books be without at least one Jules Verne? First published in the author's native France in 1863, JTTCOTE has been inspiring terrible movies and plays ever since. Stick to the original: Verne was a talented storyteller and his alternate vision for the earth's core is as imaginative as any modern-day tale requiring 3D glasses.
Little Brother, by Cory Doctorow
Easily the most contemporary title on our list, Little Brother, takes on that most time-tested trope: Boy against Totalitarian Government Agency of Oppression. Technically, a young adult novel, but it's beloved by readers of all ages. Plus, @Doctorow, like @GreatDismal, is a talented and frequent presence on Twitter.