No Isaac Asimov? "I, Robot" was admittedly slaughtered by Will Smith et al. but the book is terrific and defining in the genre. Works a lot better as short stories too.
I'm not so sure about those Heinlein books, honestly. If you like pulp, his "Starship Troopers" or "Have Spacesuit, Will Travel" are more to the point, in my opinion, and also more relevant to the rest of sci-fi.
"The Dipossessed" by Ursula K. Le Guin would be on my list, as well as David Brin's "Sundiver"-- those two have inspired so very many other authors and is the origin of a whole slew of staples, such as "uplift" and "ansible".
P D James, "Children of Men" is sorely missing. William Gibson, "Neuromancer" like pointed out above, again for defining a genre. Definitely Philip K. Dick, "Do Androids Dream of Electric Sheep?"
Also, Jules Verne, "Twenty Thousand Leagues Under the Sea". Predicting nuclear power in 1870 was pretty cool. Arguably the first "actual sci-fi" written, in that it is based on scientific ideas rather than fantastical adventure such as in Verne's other works, e.g. "Journey to the Center of the Earth"
PS. If you happen to know Swedish, this one is a MUST read:
George Johansson "Datorernas Död" [Death of the Computers] -- a brilliant cyberpunk classic written for teenagers and published a year before Gibson's Neuromancer
