“There was a time when people listened to me because I showed them how to give fight to the British without arms when they had no arms and the British Government was fully equipped and organised for an armed fight. But today I am told that my non-violence can be of no avail against the communal madness and, therefore, people should arm themselves for self-defence. If this is true, it has to be admitted that our thirty years of nonviolent practice was an utter waste of time. We should have from the beginning trained ourselves in the use of arms. But I do not agree that our thirty years' probation in nonviolence has been utterly wasted. It was due to our non-violence, defective though it was, that we were able to bear up under the heaviest repression and the message of independence penetrated every nook and corner of India. But as our non-violence was the nonviolence of the weak, the leaven did not spread. Had we adopted non-violence as the weapon of the strong, because we realised that it was more effective than any other weapon, in fact the mightiest force in the world, we would have made use of its full potency and not have discarded it as soon as the fight against the British was over or we were in a position to wield conventional weapons. But as I have already said, we adopted it out of our helplessness. If we had the atom bomb, we would have used it against the British.”

Speech to Conservative Rally at Cheltenham (3 July 1982) http://www.margaretthatcher.org/document/104989, regarding the Falkland Islands War.
First term as Prime Minister
Context: When we started out, there were the waverers and the fainthearts. The people who thought that Britain could no longer seize the initiative for herself. The people who thought we could no longer do the great things which we once did. Those who believed that our decline was irreversible—that we could never again be what we were. There were those who would not admit it—even perhaps some here today—people who would have strenuously denied the suggestion but—in their heart of hearts—they too had their secret fears that it was true: that Britain was no longer the nation that had built an Empire and ruled a quarter of the world. Well they were wrong. The lesson of the Falklands is that Britain has not changed and that this nation still has those sterling qualities which shine through our history. This generation can match their fathers and grandfathers in ability, in courage, and in resolution. We have not changed. When the demands of war and the dangers to our own people call us to arms—then we British are as we have always been: competent, courageous and resolute.

Mansion House speech (19 February 1919)
Early career years (1898–1929)
Source: Robert Rhodes James, ed., Winston S. Churchill: His Complete Speeches 1897-1963 vol. 3, 1914-1922, vol. 3 (New York: Chelsea House Publishers, 1974), 2671.
Source: Norman Rose: "Churchill: An Unruly Life", pg 146

The Love Song of J. Alfred Prufrock (1915)

The Love Song of J. Alfred Prufrock (1915)

Pokémon Theme (1997), cowritten with John Siegler.

A further quote sometimes purported to be from a speech to Congress, January 7, 1790 purportedly in the Boston Independent Chronicle, January 14, 1790, this is actually a corruption of a statement made in his first State of the Union Address, relating to the need for maintaining governmental troops and military preparedness:
:: A free people ought not only to be armed, but disciplined; to which end a uniform and well-digested plan is requisite; and their safety and interest require that they should promote such manufactories as tend to render them independent of others for essential, particularly military, supplies.
The proper establishment of the troops which may be deemed indispensable will be entitled to mature consideration. In the arrangements which may be made respecting it it will be of importance to conciliate the comfortable support of the officers and soldiers with a due regard to economy.
Misattributed, Spurious attributions

Press Conference (17 October 1987) http://www.margaretthatcher.org/document/106948, in answer to Alan Merrydew of BCTV News who asked what her response was "to a reported ANC statement that they will target British firms in South Africa?"
Third term as Prime Minister

Grover Norquist via Twitter, 02 Jan 2016, 23:12 UTC. https://twitter.com/grovernorquist/status/683425783470239744.
2015

Speech https://api.parliament.uk/historic-hansard/commons/1934/jul/13/foreign-office#column_734 in the House of Commons (13 July 1934)
The 1930s