“I write fantasy. The only science fiction I have written is Fahrenheit 451. It's the art of the possible. Science fiction is the art of the possible. It could happen. It has happened.”

The Twilight Zone, "The Fugitive" (1962).
The Twilight Zone

The Twilight Zone, "The Fugitive" (1962).
The Twilight Zone
Variant: Science fiction is the improbable made possible, and fantasy is the impossible made probable.
Context: It is said that science fiction and fantasy are two different things. Science fiction is the improbable made possible, and fantasy is the impossible made probable.

The Paris Review interview (2010)
Context: Science Fiction is the fiction of ideas. Ideas excite me, and as soon as I get excited, the adrenaline gets going and the next thing I know I’m borrowing energy from the ideas themselves. Science fiction is any idea that occurs in the head and doesn’t exist yet, but soon will, and will change everything for everybody, and nothing will ever be the same again. As soon as you have an idea that changes some small part of the world you are writing science fiction. It is always the art of the possible, never the impossible.

Introduction to the Everyman's Library edition of The Foundation Trilogy by Isaac Asimov, p. viii.

The Collected Short Fiction of C. J. Cherryh (2004) – from the introduction to "Visible Light"

In Joy Still Felt (1980), pp. 286-287
General sources

"The Imagination of Disaster" from Against Interpretation and Other Essays (1966), p. 212
Against Interpretation and Other Essays (1966)

Source: The Collected Stories of Arthur C. Clarke