hyperflare mentioned "Hitchhiker's Guide", which is a fantastic choice. I think it's the only one in these comments that I think is an unambiguous shoo-in, although OftenBen's suggestion of "Stranger in a Strange Land" is also a good one. I love Asimov and Arthur C. Clarke to death — I grew up on them — but nowadays I don't really know that I'd classify them as good sci-fi. Important, maybe, for historical reasons, but if you want to show off the best of what sci-fi can do then I think there are better choices.
Can I get any love for these?
- Fahrenheit 451 by Ray Bradbury
- Brave New World by Aldous Huxley
- Cat's Cradle by Kurt Vonnegut (I'd also accept Sirens of Titan here, but personally I like Cradle better)
- The Cyberiad by Stanisław Lem
- We by Yevgeny Zamyatin
- The Anything Box by Zenna Henderson
- The Stars My Destination by Alfred Bester (though The Demolished Man is a good choice too)
- Flowers for Algernon by Daniel Keyes
Most of these probably speak for themselves, but I do want to say that Lem is probably a lot better than you expect him to be. He's best known for Solaris, which is a dense, difficult book. The Cyberiad, by contrast, is a complete delight, and one of the funniest books I've ever read.
I also want to put in a plug for Zenna Henderson, whose short story collection The Anything Box I included in my list. She's the best sci-fi author no-one's ever heard of. In a male-dominated genre in a male-dominated time (the 1950s), when most people were writing about spaceships and lasers and robots, Henderson wrote these amazing, beautiful, touching, domestic sci-fi stories, often featuring children and families. Her work is amazing, and I really hope that one day the world will rediscover what a gem she was.