As quoted in The Making of Kubrick's 2001 (1970) by Jerome Agel, p. 300
1970s
Context: One of the biggest roles of science fiction is to prepare people to accept the future without pain and to encourage a flexibility of mind. Politicians should read science fiction, not westerns and detective stories. Two-thirds of 2001 is realistic — hardware and technology — to establish background for the metaphysical, philosophical, and religious meanings later.

“Clarke's First Law: When a distinguished but elderly scientist states that something is possible, he is almost certainly right. When he states that something is impossible, he is very probably wrong.”

Arthur C. Clarke

"Hazards of Prophecy: The Failure of Imagination" in Profiles of the Future (1962)

Perhaps the adjective "elderly" requires definition. In physics, mathematics, and astronautics it means over thirty; in the other disciplines, senile decay is sometimes postponed to the forties. There are, of course, glorious exceptions; but as every researcher just out of college knows, scientists of over fifty are good for nothing but board meetings, and should at all costs be kept out of the laboratory!

"Hazards of Prophecy: The Failure of Imagination" in Profiles of the Future (1962; as revised in 1973)
On Clarke's Laws

“This is the first age that's ever paid much attention to the future, which is a little ironic since we may not have one.”

Arthur C. Clarke

As quoted in The Peter Plan : A Proposal for Survival (1976) by Laurence J. Peter
1970s

“I will not be afraid because I understand… And understanding is happiness.”

Arthur C. Clarke book Rama Revealed

Rama Revealed

“All human plans [are] subject to ruthless revision by Nature, or Fate, or whatever one preferred to call the powers behind the Universe.”

Arthur C. Clarke book 2010: Odyssey Two

Source: 2010: Odyssey Two

“There were some things that only time could cure. Evil men could be destroyed, but nothing could be done with good men who were deluded.”

Arthur C. Clarke book Childhood's End

Guardian Angel, p. 220
2000s and posthumous publications, The Collected Stories of Arthur C. Clarke (2001)
Source: Childhood's End

“I would defend the liberty of consenting adult creationists to practice whatever intellectual perversions they like in the privacy of their own homes; but it is also necessary to protect the young and innocent.”

Arthur C. Clarke

1984: Spring (1984)
1980s

“Science can destroy religion by ignoring it as well as by disproving its tenets.”

Arthur C. Clarke book Childhood's End

1950s
Source: Childhood's End (1953), p. 15
Context: Science can destroy religion by ignoring it as well as by disproving its tenets. No one ever demonstrated, so far as I am aware, the non-existence of Zeus or Thor — but they have few followers now.

“Behind every man now alive stand 30 ghosts, for that is the ratio by which the dead outnumber the living.”

Arthur C. Clarke book 2001: A Space Odyssey

1960s
Source: 2001: A Space Odyssey (1968) "Foreword"

“Sometimes when I'm in a bookstore or library, I am overwhelmed by all the things that I do not know. Then I am seized by a powerful desire to read all the books, one by one.”

Arthur C. Clarke

“Never attribute to malevolence what is merely due to incompetence”

Arthur C. Clarke book 3001: The Final Odyssey

Source: 3001: The Final Odyssey

“… science fiction is something thathappen - but usually you wouldn't want it to. Fantasy is something thathappen - though often you only wish that it could.”

Arthur C. Clarke book The Collected Stories of Arthur C. Clarke

Source: The Collected Stories of Arthur C. Clarke

“Whether we are based on carbon or on silicon makes no fundamental difference; we should each be treated with appropriate respect.”