[lotsofmangos]

I tend to rate Mary Shelley as the earliest sci-fi author. Not just for 'Frankenstein', but also for 'The Last Man'.

I would strongly recommend tackling Issac Asimov's 'Foundation' series as one of the all time classics.

Another pretty early one to take a look at is 'We' by Yevgeny Zamyatin. It was the first book banned by the USSR and was the inspiration for Orwell's 1984.

[antimagic]

I did an "English for Engineers" course at uni (a misguided attempt at giving engineers a more rounded education - personally I was frustrated that they didn't let me take straight up Literature 101 - my roommate was an English major, and I must have written about half her essays for Lit 101, just because I found it interesting - averaged a distinction :D )

Anyway, Frankenstein was one of the cornerstone texts of that course, and you can clearly see many of the themes of later SF being developed by Shelley. We also read Dr Jekyll and Mr Hyde in that course, plus some early Australian SF (like Picnic at Hanging Rock). It was all pretty interesting, but a long way from the space opera that is one of the cornerstones of modern SF. I just don't feel like you can experience SF unless you've read some of the bigger more sweeping stuff, like Hyperion or Pandora's Star.

[baddox]

The Foundation series is certainly on my list. I have been giving series lower priority, simply because I want to go breadth-first, but I'm not confident this is a reasonable strategy, especially since I could just read the first entry and decide from there how to proceed.

I had not heard of We, but I will look into it.

[snowwrestler]

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

[lotsofmangos]

'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/

[Nux]

The Foundation series is mind blowing. I recommend reading the "Robot" series before it though as they are interlinked, particularly "Robots and Empire"; the whole thing's a joy.

[MaysonL]

If you like Asimov's Foundation series, you should look up Donald Kingsbury's Psychohistorical Crisis.