Agree with pretty much everything here. Ones I don't agree with are going on my 'books to buy' list.
By author (Not a definitive list):
Alfred Bester: 'The Demolished Man' (Man tries to get away with murder in a world of psychic detectives)
Ray Bradbury: 'Fahrenheit 451' (In a future totalitarian america, books are banned)
Phil K. Dick: 'UBIK' (In a world of nightmare commercialism, an unlikely group are trapped in a surreal, computer generated afterlife), 'Do Androids Dream of Electric Sheep?' (In a depopulated, post-apocalyptic Los Angeles, a detective-cum-hitman must decide what is real and what is not), 'A Scanner Darkly' (To combat a monstrously addictive new drug, police officers themselves must become addicts. The only problem is, the drug severs the links between the left and right side of your brain, turning you into two people, neither of which is quite sure what the hell is going on), 'Valis' (God is a computer, and the universe is mad), 'The Man in the High Castle' (The original 'The Germans won WW2' book, concerning an elusive author who has written a banned novel in which he postulated what might have happened if the Germans had lost. Reportedly written using the I Ching), 'Flow My Tears, The Policeman Said' (A drug is developed that alters not only your perception of reality, but everyone elses as well)
Philip Jose Farmer: 'The Riverworld Series (To Your Scattered Bodies Go, The Fabulous Riverboat, The Magic Labyrinth, The Dark Design)' (Every man and woman that ever lived is resurrected along an endless river, incapable of death, with all their material comforts cared for, but no materials with which to establish a civilisation. High adventure, shitloads of sex and deep, spiritual themes ensue.)
Ursula K LeGuin: 'The Left Hand of Darkness' (Thought-provoking novel that examines what gender means in a world of hermaphrodites), 'The Word For World Is Forest' (Humans blatantly disrespect the shamanic beliefs of an alien race and exploit them and their vast hardwood forests with willful abandon. Aliens rise up. Humans get owned.)
Harry Harrison: 'Bill The Galactic Hero' (A vicious and cynical satire on the insanity of War), 'The Stainless Steel Rat' (The greatest criminal in the Galaxy becomes it's most unorthodox cop. You cannot help but love Slippery Jim DeGriz)
Also worth reading by Harrison is 'Star Smashers of the Galaxy Rangers', but only if you've ever read the Lensman series.
Aldous Huxley: 'Brave New World' (Drugs and mindless liesure render life meaningless in a dystopia of terrors far more subtle and unnerving than 1984)
Richard Jefferies: 'After London' (The first post-apocalyptic novel)
Anne McCaffery: 'The Ship Who Sang' (A pinnacle of hippie sci-fi not even LeGuin could approach. Crippled child is hardwired into a space-ship and roves the galaxy adventuring, exploring feminism and singing Bob Dylan songs)
Mary Shelley: 'Frankenstein' (Probably the first thing really deserving the title 'Sci-fi'. And still brilliant.)
Olaf Stapledon: 'The Star Maker' (Philosophical space opera that spans the life of the universe. The word 'Epic' is redefined.)
HG Wells: 'The War of the Worlds' (Wells laughs at imperialism as the Martian tripods tower over London), 'The Time Machine' (The Future's not worth knowing about)
Gene Wolf: 'The Book of the New Sun (The Shadow of the Torturer, The Claw of the Conciliator, The Sword of the Lictor, The Citadel of the Autarch)' (Sci-fi and fantasy meld in a work of vast imagination set in earths distant, dying days).
John Wyndham: 'The Chrysalids' (In a post-apocalyptic world, the greatest crime is deviation. I always maintain that this is Wyndhams best book), 'The Midwich Cuckoos' (Aliens impregnate all the women in a small English village. Creepy glowing eyed children proliferate), 'The Day of the Triffids' (Satellite weapons strike almost everyone blind. Unchecked, mutant plants go out of control and eat people.)
Sci-fi short stories you should attempt to acquire:
Jerome Bixby - It's a Good Life (Basis for the classic Twilight Zone episode)
Phil K Dick - The Second Variety (Paranoia reigns in a war between machines and humans. Primary source for Terminator and the Matrix.)
Walter M. Miller Jr. - Crucifixus Etiam (Frontier religion on a hellish, half-terraformed Mars)
Fredrick Pohl - The Tunnel Under the World (People are enslaved to market researchers)
Robert Sheckley - Specialist (Humanity finds its place in the universe)
Raccoona Sheldon - The Screwfly Solution (Aliens exterminate the human race without laying a finger on us. Utterly terrifying.)
Cordwainer Smith - The Game of Rat and Dragon (There are some really nasty things out there in interstellar space)
HG Wells - The Land Ironclads (HG Wells predicts the shape of future war in an extremely uncanny way)
I'd recommend 'The Oxford Book of Science Fiction Stories' (Ed: Tom Shippey) and 'The Golden Age of Science Fiction' (Ed: Kingsley Amis) as a starting point for these, though some, such as Tunnel Under The World and The Specialist, are in practically everything. I think I have the Specialist in four different collections.
I've tried to mainly keep to old stuff, mainly 70's and earlier, with this list, and of course there's a lot missed out even then. I just kinda got bored :/