1) When a distinguished but elderly scientist states that something is possible, he is almost certainly right. Corollary: When he states that something is impossible, he is very probably wrong.
2) The only way to discover the limits of the possible is to venture beyond them into the impossible.
3) Any significantly advanced technology is indistinguishable from magic.
The third law is most famous, but I'm personally fondest of the first one. I think it's particularly important to remember in writing science fiction. A lot of writers slam "bad science" in stories, and they have a point. But beyond the need to describe things like loss of gravity or the effects of faster-than-light travel accurately, there is the simple fact that we today cannot predict what will be possible in a hundred years, or a thousand. I don't care how an internal combustion engine works, I care what it means to a person to own a car.
I've read several obituaries of Clarke and liked the one on Yahoo best.