“The danger of asteroid or comet impact is one of the best reasons for getting into space … I'm very fond of quoting my friend Larry Niven: "The dinosaurs became extinct because they didn't have a space program. And if we become extinct because we don't have a space program, it'll serve us right!"”

"Meeting of the Minds : Buzz Aldrin Visits Arthur C. Clarke" by Andrew Chaikin (27 February 2001) http://web.archive.org/web/20010302082528/http://www.space.com/peopleinterviews/aldrin_clarke_010227.html
2000s and attributed from posthumous publications
Context: The danger of asteroid or comet impact is one of the best reasons for getting into space … I'm very fond of quoting my friend Larry Niven: "The dinosaurs became extinct because they didn't have a space program. And if we become extinct because we don't have a space program, it'll serve us right!"

Source: The Sky Is Not the Limit: Adventures of an Urban Astrophysicist

Anonymous

Headline quote at the beginning of Chapter 3, "Mining the Heavens," page 54.
The Future of Humanity (2018)

In a Reddit IAmA. http://www.reddit.com/r/IAmA/comments/r62jp/iama_nasa_astronaut_that_recently_returned_to/c437ubd (2012)
An earlier similar quotation can be found in:
The dinosaurs became extinct because they didn't have a space program. And if we become extinct because we don't have a space program, it'll serve us right!
By Larry Niven As quoted by Arthur C. Clarke in "Meeting of the Minds : Buzz Aldrin Visits Arthur C. Clarke" by Andrew Chaikin (27 February 2001) http://web.archive.org/web/20010302082528/http://www.space.com/peopleinterviews/aldrin_clarke_010227.html

On the definition of space: Reach Into Space http://www.time.com/time/magazine/article/0,9171,892531,00.html, Time, 1959-05-04.

Review of “Eyes of Amber”, by Joan D. Vinge (as anthologized in New Women of Wonder, edited by Pamela Sargent http://jamesdavisnicoll.com/review/yet-more-sf-about-women-by-women, 2015
2010s
Context: There’s a rule I used to call The Niven Rule but which I just now have decided to call the Rusting Bridges rule. It came to me after reading Niven’s “All The Bridges Rusting.” In this story, humans have by the early 21st century explored the Solar System and sent not just one but two crewed ships to Alpha Centauri … despite which the characters moan endlessly about the dire state of the space program. “Eyes of Amber” would be another example of the Rusting Bridges [Rule]: No matter how much the space program you actually have has achieved, whether it’s first contact with aliens or trips to nearby stars, it can never have achieved as much as the space programs you can imagine would have achieved in its place, given that imaginary programs aren’t limited by issues of politics, funding, or engineering.

Playboy interview (1996)
Context: If NASA's budgeters could be convinced that there are riches on Mars, we would explode overnight to stand on the rim of the Martian abyss. We need space for reasons we have not as yet discovered, and I don't mean Tupperware. … NASA feels it has to justify everything it does in practical terms.
And Tupperware was one of the many practical products that came out of space travel. NASA feels it has got to flimflam you to get you to spend money on space. That's B. S. We don't need that. Space travel is life-enhancing, and anything that's life-enhancing is worth doing. It makes you want to live forever.

On the dangers and importance of the mission of going to the moon in "Gemini : A Personal Account of Man's Venture Into Space (1968) by Virgil I. Grissom
Context: If we die we want people to accept it. We are in a risky business, and we hope that if anything happens to us, it will not delay the program. The conquest of space is worth the risk of life. Our God-given curiosity will force us to go there ourselves because in the final analysis, only man can fully evaluate the moon in terms understandable to other men.

In Search of Memory (2006)