Some iconic science fiction books that can stand alone:

    Asimov: The Gods Themselves
    Clarke: Childhood's End, Rendezvous with Rama
    Herbert: Dune, Whipping Star
    Bradbury: Fahrenheit 451
    Bester: The Demolished Man, The Stars My Destination (also called "Tiger, Tiger")
    Niven: Ringworld
    Niven and Pournelle: The Mote in God's Eye, Footfall
    Gibson: Neuromancer
    Stephenson: Snow Crash, The Diamond Age
    Bear: The Forge of God, Eon
    Sagan: Contact
    van Vogt: The Voyage of the Space Beagle
    Lem: Solaris
    Atwood: The Handmaid's Tale
    LeGuin: The Left Hand of Darkness
    Lewis: Out of the Silent Planet

Some of these are the beginnings of series or have sequels, or exist in a larger continuum of stories. But each can be read and appreciated on their own. If you find one you really like, it's not hard to see if there are more in a series or sequel.

Edit: formatting

'We' is excellent. It is also a lot funnier than '1984', though that is not hard.

Also, you have to hit the short-story collections to find some of the best sci-fi. Off the top of my head, Asimov, Dick, Bradbury, Clarke, Gibson, Banks, Egan, all wrote some of their best work in short form.

And, just thinking about really early stuff, 'Flatland' by Edwin Abbott is another you should really take a look at.

If you want to try any recent stuff, Alastair Reynolds and China Miéville are both excellent authors.

edit - oh, and just read everything ever written by Neal Stephenson.

edit2 - and Bruce Sterling. His tumblr blogs aren't bad either.

http://brucesterling.tumblr.com/

http://wolfliving.tumblr.com/