“Why I am a Free Trader,” Chapter I in T.W. Stead’s journal Coming Men on Coming Questions (April 13, 1905), bottom p. 9.
Early career years (1898–1929)

Speech given at Harrow School, Harrow, England, October 29, 1941. Quoted in Churchill by Himself (2008), ed. Langworth, PublicAffairs, 2008, p. 23
The Second World War (1939–1945)
Source: Never Give In!: The Best of Winston Churchill's Speeches
Context: Never give in — never, never, never, never, in nothing great or small, large or petty, never give in except to convictions of honour and good sense. Never yield to force; never yield to the apparently overwhelming might of the enemy.

On Stanley Baldwin, as cited in Churchill by Himself (2008), Ed. Langworth, PublicAffairs, p. 322 ISBN 1586486381
Also quoted by Kay Halle in Irrepressible Churchill: A Treasury of Winston Churchill's Wit http://books.google.com/books?id=b0MTAQAAIAAJ&q=%22Occasionally+he+stumbled+over+the+truth+but+hastily+picked+himself+up+and+hurried+on+as+if+nothing+had+happened%22&pg=PA133#v=onepage (1966).
The 1930s
Variant: Men occasionally stumble over the truth, but most of them pick themselves up and hurry off as if nothing ever happened.

Variant: I am easily satisfied with the very best.

Attribution debunked in Langworth's Churchill by Himself. The earliest close match located by the Quote Investigator is from the 1953 book How to Say a Few Words by David Guy Powers.
Misattributed
Variant: Success is the ability to go from one failure to another with no loss of enthusiasm.
Source: 1953, How to Say a Few Words by David Guy Powers, Quote p. 109, Doubleday & Company, Garden City, New York. Referenced by Quote Investigator http://quoteinvestigator.com/2014/06/28/success

As cited in The Forbes Book of Business Quotations (2007), Ed. Goodwin, Black Dog Publishing, p. 168, ISBN 1579127215
Post-war years (1945–1955)

Attribution debunked in Langworth's Churchill by Himself. First known appearance is in a 1992 usenet post https://groups.google.com/forum/message/raw?msg=rec.arts.comics.misc/EMj3ZowKq1U/E0dsEBwdZEgJ.
Misattributed
Source: Google books link https://books.google.com/books?id=vbsU21fEhLAC&q=average+voter#v=snippet&q=average%20voter&f=false

Variant: A kite flies against the wind, not with it.

Lord Mayor’s Banquet, Guildhall, London (9 November 1954) The Unwritten Alliance, page 195, Columbia University, NY (1966),page 195,
Post-war years (1945–1955)

Variant: A fanatic is one who can't change his mind and won't change the subject.

In the House of Commons, February 28, 1906 speech South African native races http://hansard.millbanksystems.com/commons/1906/feb/28/south-african-native-races#S4V0152P0_19060228_HOC_307
The Second World War (1939–1945)
Variant: Where there is great power there is great responsibility
Context: I submit respectfully to the House as a general principle that our responsibility in this matter is directly proportionate to our power. Where there is great power there is great responsibility, where there is less power there is less responsibility, and where there is no power there can, I think, be no responsibility.

First mentioned as "Continuous effort — not strength or intelligence — is the key to unlocking and using our potential." according to Quote Investigator in the 1981 book The Reflecting Pond: Meditations for Self-Discovery by Liane Cordes, Quote Page 89, Hazelden Publishing, Center City, Minnesota. For further research on this quote see: Quote Investigator (August 31, 2013): Continuous Effort — Not Strength or Intelligence — Is the Key to Unlocking and Using Our Potential Winston Churchill? Liane Cordes? Liane Cardes? Apocryphal? Archived http://archive.is/E0M12 on June 2, 2020.
Source: https://quoteinvestigator.com/2013/08/21/effort/ from the original

Source: Wealth, War, and Wisdom

In Reader's Digest (December 1954).
Post-war years (1945–1955)
Variant: An appeaser is one who feeds a crocodile, hoping it will eat him last.