Important Science Fiction
I'm not looking merely for works that you like, but works that have had some sort of impact, either on you personally or the genre in general. I'll start with those I believe to have had the greatest influence on the genre.
There is, I believe, one author who has done as much to shape science fiction as Tolkien has done for fantasy. This would be Isaac Asimov. He gave us the Three Laws of Robotics . . . he gave us the very /word/ robotics. Almost every modern image of a robot traces back to something from Asimov's works (except for the evil, megalomaniacal ones). So, I'll start with his Robot novels:
I, Robot
The Rest of the Robots (This is an anthology including numerous short stories and also the two complete novels The Caves of Steel and The Naked Sun. The Caves of Steel is important not only for being the first of the Daneel Olivaw novels, but also for introducing the science-fiction mystery.)
The Robots of Dawn
Robots and Empire
These last two continue the Daneel Olivaw novels, after the death of Elijah Bailey.
The Foundation books are equally important. I will go ahead and list all those Asimov wrote, in the order in which they take place, and then discuss a few distinctions among them.
Prelude to Foundation
Forward the Foundation
Foundation
Foundation and Empire
Second Foundation
Foundation's Edge
Foundation and Earth
Foundation, Foundation and Empire, and Second Foundation comprise the so-called Foundation Trilogy. These were first written as a series of short stories, published in magazines, and later collected into those three books. The two sequels were written years later, by popular (and publisher) demand, after Asimov himself had expressed no further desire to continue with that universe. I believe the prequels were written even later than that, probably should not be read until after reading the trilogy, and may be safely skipped entirely. There is also a so-called Second Foundation Trilogy, three novels written in recent years by three separate authors, none of whom are Asimov. Please, please don't read these. You have been warned. (I didn't even bother to list them.)
And then there are several important short stories by Asimov. When seeking out these, make sure you find the original Asimov short stories, not the novelizations by Robert Silverberg. (One of those has been made completely butchered into a movie.) The short stories tend to be the title story of anthologies, and the rest of the stories tend to be worth reading as well. Hey, it's Asimov.
"The Bicentennial Man"
"Nightfall"
"The Ugly Little Boy"
Minor spoiler for "The Bicentennial Man" perhaps, though since there's a movie most people probably already know this much:
There's two more authors I want to discuss briefly, but this wall of text is already long enough. I'll make separate posts later, probably in a few hours. Meanwhile, feel free to discuss.

Comments
Robert Anson Heinlein
Ah, Heinlein. How do I love thee? Let me count the ways . . . .
But it isn't my personal enjoyment of his works that I wanted to discuss, but his influence on the genre as a whole.
What Asimov did for robots, Heinlein did for space exploration. Cities on the moon, space habitats, asteroid mining . . . see Heinlein. Oh, sure, Asimov did some of that, too, and Arthur Clarke, and Larry Niven played with it a lot, and many others. But Heinlein . . . Heinlein was the acknowledged master. Important works, in suggested reading order:
The Past Through Tomorrow. It's a major anthology . . . at the very /least/ read "The Man Who Sold the Moon", "The Green Hills of Earth" and "Methuselah's Children". We /need/ a Delos D. Harriman; I've become convinced that nothing else will get us off this planet and firmly established elsewhere.
Time Enough for Love.
The Moon is a Harsh Mistress.
The Number of the Beast.
The Cat Who Walks Through Walls.
To Sail Beyond the Sunset.
And, of course, Stranger in a Strange Land. If you read nothing else mentioned in this thread . . . read Stranger in a Strange Land. No description I give could possibly do it justice. Read it before Number of the Beast.
Heinlein also played with the concept of time travel a lot. This shows up in Time Enough for Love, The Number of the Beast, and most of his later novels, but also in several of his short stories. These, and other stories, have been collected in the anthology The Other Science Fiction of Robert A. Heinlein.
Glory Road is in some respects more of a fantasy than pure science fiction. Oscar Gordon even says something to the effect of "I can't believe everything I encountered will someday be built by IBM once Bell Labs tells them how." (I'm probably misquoting that; it's been way too long since I've read it.) It's perhaps not as significant as his other works, but it's a very fun romp. Besides, Lady V would probably take a sword to me if I didn't mention it.
An interesting reply.
Lady V had this to say in response.
*puts on literary nerd hat*
I would like to add that, more than any influence he had on topics in science fiction-- and yes, he was the champion of space travel-- he greatly influenced the style of the genre. He made it readable, accurate (two things which had never gone hand in hand before), and respectable. He--not single-handedly, but nearly so-- took science fiction out of the pulps and made it into something people weren't ashamed to admit they read and enjoyed.
*removes literary nerd hat*
His influence goes far beyond that, though. Stranger in a Strange Land made him a voice of the Free Love movement in the sixties, though God knows he never intended to be such. If you want to understand how I feel about love, jealousy, and God, read Stranger. It goes a long way towards explaining much of how I think. (I am fairly certain that I believed as I do before I read it; it came late in my life, as far as Heinlein goes. I believe it merely put into words what I already thought, though I am sure in some ways it altered my way of thinking.)
On the other hand, Starship Troopers is, as far as I know, the only science fiction novel on the required reading list for all of the US Armed Forces academies. If you have never read it, please, do not judge it by the movie; the book is in depth political and social commentary, where the movie... I have a lot of friends who saw it solely for the shower scene. Starship Troopers is the reason I occasionally (read: once a year or so) think seriously about joining the military.
I like citing those two because they are as far apart as you might imagine two books of the same genre could be, and yet... they have at their core some interesting similarities. I dare you to read both and see what I mean.
As for Glory Road... it is, now and ever, my favorite novel. Period. I do not claim it is the best or most significant he ever wrote; I know that others outshine it. But it speaks to me, very deeply. And it isn't the action, it isn't the main part of the story. It's the part that Heinlein included that other writers would have left out: after saving the world and marrying the princess, what is left for the hero? Oscar eventually finds that he cannot enjoy the rewards he supposedly fought for; what good are riches, when he feels useless? As he goes home and discovers that he no longer belongs there, my heart breaks; I know exactly how he feels, and I do not have the excuse of ever having been anywhere else. And when he, in the end, goes out to go adventuring once more, I long more than anything to go with him. And though it always makes me a little sad that I cannot, the last line always brings a smile to my face:
"Got any dragons you need killed?"
(I could write a whole essay on why that last line is brilliant. I will refrain. I think I've rambled enough.)
I almost included Starship Troopers on my must read list. Probably should have. Space Cadet is another one in somewhat similar vein, though intended for a younger audience. His juvenile works are just as well written, and just as influential, as what he wrote for adults.
Lady V also . . .
found the quote I was looking for before. "But I would be disappointed if everything I saw turned out to be something Western Electric will build once Bell Labs works the bugs out. There ought to be some magic, somewhere, just for flavor."
And then we got to discussing the first lines of some of Heinlein's works.
Have Spacesuit, Will Travel: "You see, I had this spacesuit."
Stranger in a Strange Land: "Once upon a time there was a Martian named Valentine Michael Smith."
To Sail Beyond the Sunset: "I woke up in bed with a man and a cat. The man was a stranger; the cat was not."
Number of the Beast: "'He's a Mad Scientist and I'm his Beautiful Daughter.' It was the oldest line from the pulps. She wasn't old enough to remember the pulps."
Glory Road: "I know a place where there is no smog and no parking problem and no population explosion . . . no Cold War and no H-bombs and no television commercials . . . no Summit Conferences, no Foreign Aid, no hidden taxes--no income tax. The climate is the sort that Florida and California claim (and neither has), the land is lovely, the people are friendly and hospitable to strangers, the women are beautiful and amazingly anxious to please--
"I could go back. I could--"
Can anyone read those lines and not want to find out what happens next?
Arthur C. Clarke
(I know I posted this over Christmas, which might account for the dearth of replies. But is anyone even reading it? Well, one more author, and then I'll shut up for a while.)
Arthur Clarke's greatest influence is perhaps the statement that has come to be known as Clarke's Law: "Any sufficiently advanced technology is indistinguishable from magic." I think it was David Brin who gave us the contrapositive, which was the only good thing to come out of that so-called Second Foundation Trilogy: "Any technology distinguishable from magic is insufficiently advanced." And Mercedes Lackey used the converse in one of her urban fantasies: "Sufficiently complex magic is indistinguishable from technology."
But Clarke succeeded at something Heinlein only attempted: bringing science fiction--hard science fiction--to the movie theater. Heinlein did make a valiant effort, but has anybody even heard of, much less seen, Destination: Moon? I've read the screenplay; it was part of an anthology of his works.
Ah, but 2001: A Space Odyssey . . . love it or hate it, seen it or not, I believe everyone here will have at least heard of it. Most people can probably quote at least one line from it. ("I'm sorry, Dave; I'm afraid I can't do that.")
I do admit that there are some elements to that movie that may not be entirely clear without reading the book, particularly the birth of the Star Child at the end and other scenes involving the monoliths. However, Clarke himself considered the movie, not the book, to be canonical; when he wrote 2010, he followed the continuity of the movie.
Some might question my calling it hard science fiction, perhaps legitimately. The aliens have near-instantaneous travel over immense distances, and, in the sequel, go so far as to turn the planet Jupiter into a small star. See Clarke's law, above.
But ignore the monoliths for now, and consider only what the humans have done. I have seen only one complaint on the technical accuracy of the movie: the distance between Earth and Jupiter is not great enough to show movement of the starts during the trip.
Other notable science fiction movies--Star Wars, Star Trek, etc.--tend to be science fantasies at best, if not outright fantasies.
With two exceptions that I can name, everything depicted as having been built by humans /could/ be built, most probably with today's technology. Most of the obstacles are political and economic, not technical. And a sufficient budget would overcome any technical obstacles that do remain. All right, a manned mission to Jupiter (Saturn, in the book) might be stretching things, but only because we don't have the infrastructure in place to support it. We can build that infrastructure. The space habitats, the bases on the moon . . . we could almost certainly do that, if only people would spend the money to get started.
But we don't yet know enough to do suspended animation, if it's even possible. And the other exception is the Hal 9000 computer, or, rather, the AI software for it.
Ah, Hal. Much maligned Hal. You were only trying to do what you were told . . . it's not your fault you were given two conflicting sets of instructions that couldn't possibly both be carried out. (This is perhaps another thing more clear in the novel than the movie.)
This is the other thing for which 2001 is notable: the computer driven homicidally insane by a programming conflict. Oh, sure, the archetype of a man-made intelligent being turning against its maker goes back at least to Mary Shelley's Frankenstein. But Clarke gave us a logical reason why a machine, built and programmed by humans, would deliberately kill humans when it was not intended to do so.
Okay, enough about 2001. Like Asimov and Heinlein, Clarke also wrote numerous short stories. (In fact, the concept of the monoliths from 2001 comes from one such, called "The Sentinel".) There's one to which I want to direct specific attention: "The Nine Billion Names of God". Unfortunately, I can't say why I'm directing attention to it without spoiling it.