(Science fiction, not San Francisco.) Having never really experienced the genre much, I have recently been trying to assemble (and eventually read) a list of influential and quintessential science fiction books, and while my informal research into the beginnings of sci-fi as an identifiable genre led me to earlier authors like Verne and Wells, I had never heard of this fellow or this magazine.
By the way, if one wants to read a quick standalone sci-fi novel, I just finished Heinlein's The Moon is a Harsh Mistress, and I can't recommend it strongly enough.
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.
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.
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.
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.
'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.
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.
SF is a broader church than you might imagine from the outside, and many people (including me!) will give you a list of "classics" that are actually quite a narrow slice because that's the subgenre they're into. I'd recommend starting from something like the Locus top 100; populism has its problems but will at least ensure you don't completely miss any major areas.
So, because I haven't seen it mentioned, go check out anything by Harlan Ellison. I will strongly suggest the Shatterday or Stalking the Nightmare anthologies. Those stories have some fucking teeth.
Science fiction (or speculative fiction, if you're feeling highbrow) is probably one form where I still regularly buy "Year Best <whatever>" anthologies...it's a form that is benefited heavily from short stories, because scifi is about the ideas, not so much the characters. Good science fiction has both, of course, but must have good ideas--lots of stories happen that have decent character development but the ideas stink.
I also would strongly recommend the Pump Six anthology by Paolo Bacigalupi; it's biopunk, I suppose, but pretty solid and plays well with the ideas of being past Peak Energy.
I'm a big Heinlein Fan. I strongly recommend you read his other big famous works, "Starship Troopers" and "Stranger in a Strange Land." After that you can dig deeper into his bibliography, but I'd consider those three to be essential reading.
I recently finished "Roadside Picnic" by Arkady and Boris Strugatsky and I loved it. Makes me curious to read other sci fi from the Soviet world.
Look for Macmillan's Best of Soviet Science Fiction series, published in the early 1980s. It's a mix of novels and short story collections. For shorts, I particularly recommend World's Spring, New Soviet Science Fiction, and Ballad of the Stars.
A long time ago, I read that Asimov's short story 'Nightfall' was considered the finest short SF of all time, but I respectfully disagree. Nine Minutes, by Genrikh Altov, is that story for me. Link: http://www.altshuller.ru/world/eng/science-fiction4.asp
Also - a truly awesome novel - 'Self Discovery', by Vladimir Savchenko (also in the Macmillan series). (Link: http://lib.ru/RUFANT/SAWCHENKO/savchenko_selfdiscovery_ok-en...) It has one of the most compelling, and fascinating, descriptions of AI I've ever come across. As Theodore Sturgeon writes in the introduction, 'described with such realism that one is tempted to apply for a grant, build it, and check it out.'
Imo forever war is amazing, but stranger in a strange land devolves into bizarre fantasy. I'd strongly recommend the former if you're more interested in hard sci fi and the implications of real accurate (ish) relativistic travel.
Seconding this... Forever War is probably some of the most readable, non-America-Fuck-Yeah military sci-fi I've read--another good one is Armor.
If you want more military sci-fi, check out the Hammer's Slammers series by David Drake (tank company in spaaaaaace, but not the stupid Bolo stuff); he also had one anthology that was very nearly solid cyberpunk surveillance dystopia, Lacy and His Friends.
When I was 12 or 13 I discovered E E "Doc" Smith, John W Campbell and Philip Nowlan. I'd been reading more contemporary authors like Heinlein and Andre Norton, and the sheer "noise" of these older books were astonishing. What teenage boy doesn't like antimatter planets being flung at Boskonian space pirate outposts, or spaceships powered by solidified light? For a while I loved them.
I still have fond memories of Smith's galaxy-spanning Skylark series, the planet bashing swagger of the Lensman series, and Campbell's unapologetic "super science", but the prose has not aged well and I find them difficult to read now. I feel a little sad about that.
I can still recommend Smith's The Skylark of Space and Skylark Three, and Campbell's The Moon is Hell, but not much else.
Larry Niven's short story collections are well worth picking up. His first is 'Inconstant Moon' and it's where I first discovered him. Some of the stories later developed into key parts of his Known Space cycle of short stries and novellas. They're all great stuff, but IM is the starting point.
If you like it you can check out the rest, if not then they're only short stories so not too much of an investment in time.
By the way, if one wants to read a quick standalone sci-fi novel, I just finished Heinlein's The Moon is a Harsh Mistress, and I can't recommend it strongly enough.