I think everyone interested in Sci-Fi should read Stranger in a Strange Land and Starship Troopers. They're very different books, and there is much to disagree with either one for most people, but they have interesting ideas and what I think is rather skillful writing. You'll disagree with one or both, but it's worth the thoughts that go into it.
I also recommend Dragon's Bane by Barbara Hambly. And, believe it or not, Jeffe once gave me a book called Cowboy Feng's Space Bar and Grill that turned out to be a very good book, and not a silly one either. It's not a classic, but it's a good read.
There's also the ever popular Narnia series (you've probably read it), but C.S. Lewis also did a sci-fi trilogy, the first of which was called Out of the Silent Planet which, while curious in approach to technology and even more overt in it's Christianity than Narnia, was a really good read.
Finally, Lloyd Alexander's Prydain Chronicles, starting with The Book of Three. These are the first books I read several times. So I recommends them if you haven't read them.