I love classic scifi like Asimov and Harry Harrison. I have used Asimov's Three Laws of Robotics in class, where students tried to find potential problems with those laws and come up with a fourth law that could solve them. Harry Harrison (author of "Make Room, Make Room!", which became the film Soylent Green) is rarely read nowadays, but his stuff all features jaunty heroes whose hearts of gold are hidden by their gambling or theiving ways. Most of them are pretty short, and they're lots of fun.
My all-time favorite author is Marion Zimmer Bradley, who is mostly known for her bestsellerThe Mists of Avalon but was incredibly prolific and wrote an astonishing number of books. I particularly like her Darkover series, set in a world where the top technology is psi power, not machine/computer technology. It does a great job of using the alternative world to examine conventions in our own world and history, particularly those having to do with interpersonal communication, gender relations, and family loyalty.
At the moment, I'm loving Naomi Novik's Temeraireseries, which I haven't taught but I imagine would be great in a classroom with students studying European history. It's an alternative history book centered on a retelling of the Napoleanic wars, but with one crucial difference--England and France both have an air force made up of dragons. Pretty cool stuff!
It seems to me that you'll either choose works based on length, fame/ influence, or student popularity.
I agree with the above responses that Bradbury is a great introduction to science fiction, especially The Martian Chronicles, but particularly since he wrote many short stories. Ursula K. LeGuin's "The Ones that Walk Away From Omelas" is a strong sci fi/ dystopia short story.
I am especially impressed to see Crichton mentioned since he's not shelved with science fiction writers, but I agree that his work should be considered science fiction. Of his novels, my favorite is either Jurassic Park or Sphere. A lot of students love reading his novels as well. I think my most popular classroom library science fiction has been Ender's Game by Card.
As for famous works, you should probably look at Asimov or authors that are older still. Arthur C. Clarke's 2001: A Space Odyssey is also a classic.
If you were interesting in trying something more contemporary, you should probably read Robert Charles Wilson.
Alas, Babylon is a great book, as is Farenheit 451. Anything by Ray Bradbury is oh-so-cool. I also like teaching "The Shawshank Redemption" and other short stories by Stephen King. SR is really sci-fi, but kids love it that King wrote it and we can watch the film afterward for comparison and argument about choices in camera angles, lighting, delivery.
I think the best science fiction doesn't just entertain but makes you think about what might be possible. For instance, Crichton's Andromeda Strain was written long before 9/11, but it makes us think about biological threats. Bradbury's There Will Come Soft Rains is another story that makes you think about what the future might be like.
You also need to decide how to define science fiction. Is The Giver science fiction? How about The Little Prince?