Deep quotes

Variant: A person who never made a mistake never tried anything new.

'Where Do We Go From Here?" as published in Where Do We Go from Here : Chaos or Community? (1967), p. 62; many statements in this book, or slight variants of them, were also part of his address Where Do We Go From Here?" which has a section below. A common variant appearing at least as early as 1968 has "Returning violence for violence multiplies violence..." An early version of the speech as published in A Martin Luther King Treasury (1964), p. 173, has : "Returning hate for hate multiplies hate..."
1960s
Source: A Testament of Hope: The Essential Writings and Speeches
Context: The ultimate weakness of violence is that it is a descending spiral, begetting the very thing it seeks to destroy. Instead of diminishing evil, it multiplies it. Through violence you may murder the liar, but you cannot murder the lie, nor establish the truth. Through violence you may murder the hater, but you do not murder hate. In fact, violence merely increases hate. So it goes. … Returning hate for hate multiplies hate, adding deeper darkness to a night already devoid of stars. Darkness cannot drive out darkness: only light can do that. Hate cannot drive out hate: only love can do that.

First attibution is to Ralph Bergstresser who claims to have heard this from Tesla in a conversation "following an experience with the Maharaja's son".
Disputed
Source: Coments From The Inventor of the Purple Harmony Plates http://www.bibliotecapleyades.net/ciencia/esp_ciencia_universalenergy02.htm,

Source: Meditations

Georges Duhamel in THE HEART'S DOMAIN (1919). As it was composed in French, the wording in English may vary in translation. Theodore Geisel / Dr. Seuss was born in 1904, and would have been about 15 years old at the time that it was published. The full text can be found at the link below: We do not know the true value of our moments until they have undergone the test of memory. Like the images the photographer plunges into a golden bath, our sentiments take on color; and only then, after that recoil and that trans-figuration, do we understand their real meaning and enjoy them in all their tranquil splendor.
Misattributed

Variant: When I was 5 years old, my mother always told me that happiness was the key to life. When I went to school, they asked me what I wanted to be when I grew up. I wrote down ‘happy’. They told me I didn’t understand the assignment, and I told them they didn’t understand life.

Books, Coningsby (1844), Lothair (1870)
Variant: Action may not always bring happiness; but there is no happiness without action.

Source: The Picture of Dorian Gray

Also found with the alternative spelling: Everything is okay in the end. If it's not okay, it's not the end
Found anonymously on Usenet in 2000 https://groups.google.com/forum/message/raw?msg=alt.support.divorce/gKiyfcAYreo/jjuc6KTu_NAJ. First known attribution to Lennon is from 2011 https://groups.google.com/forum/message/raw?msg=stow-ma-apple-barn/45MNk9KiGsY/vaq6pr8hgI0J.
Disputed
Variant: Everything is OK in the end. If it's not OK, it's not the end.

Source: You Learn by Living (1960), p. 29–30
Context: You gain strength, courage and confidence by every experience in which you really stop to look fear in the face. You are able to say to yourself, "I have lived through this horror. I can take the next thing that comes along." … You must do the thing you think you cannot do.

Variant: It is easier to build strong men, than to repair broken ones.
Source: Narrative of the Life of Frederick Douglass

Quiet Strength (2000)

Variant: Some people want it to happen, some wish it would happen, and others make it happen.

The Soul of Man Under Socialism (1891)
Context: With the abolition of private property, then, we shall have true, beautiful, healthy Individualism. Nobody will waste his life in accumulating things, and the symbols for things. One will live. To live is the rarest thing in the world. Most people exist, that is all.

This is actually a quotation http://books.google.com/books?id=FUIHmRHf8SUC&lpg=PA130&dq=%22not%20on%20fighting%20the%20old%20but%20on%20building%20the%20new%22&pg=PA130#v=onepage&q=%22not%20on%20fighting%20the%20old%20but%20on%20building%20the%20new%22&f=false from a character named Socrates in Way of the Peaceful Warrior: A Book that Changes Lives http://en.wikipedia.org/wiki/Way_of_the_Peaceful_Warrior, by Dan Millman.
Misattributed

As quoted in Our Precarious Habitat (1973) by Melvin A. Benarde, p. v

Variant: Remember to look up at the stars and not down at your feet. Never give up work. Work gives you meaning and purpose and life is empty without it. If you are lucky enough to find love, remember it is there and don't throw it away.

We Bereaved (1929)

Shared on her Facebook page https://www.facebook.com/MayaAngelou/posts/10150251846629796, July 4, 2011

As quoted in Our Precarious Habitat (1973) by Melvin A. Benarde, p. v
Context: Nothing in life is to be feared, it is only to be understood. Now is the time to understand more, so that we may fear less.

Variant: I now see how owning our story and loving ourselves through that process is the bravest thing that we will ever do.
Source: Rising Strong

Variant: Those who know, do not speak, those who speak, do not know.
Source: Tao Te Ching, Ch. 56

Variant: Be a rainbow in somebody else's cloud.
Source: Letter to My Daughter

Mildred Pierce

Source: Hamlet, Act III, scene i.

The Note Book of Elbert Hubbard (1927)
Variant: The greatest mistake you can make in life is to be continually fearing you will make one.

Letter to his son Eduard (5 February 1930), as quoted in Walter Isaacson, Einstein: His Life and Universe (2007), p. 367
1930s

Source: Doctor Sleep

Variant: You can make more friends in two months by being interested in them, than in two years by making them interested in you.
Source: How to Win Friends and Influence People (1936), p. 52 (in 1998 edition)

Source: Going Bovine

Source: I Have a Dream: Writings and Speeches That Changed the World

Variant: The best and most beautiful things in the world cannot be seen or even touched. They must be felt with the heart.
Variant: The best and most beautiful things in the world cannot be seen, nor touched... but are felt in the heart.

Variant: You must give up the life you planned in order to have the life that is waiting for you.

Variant: Always forgive your enemies — nothing annoys them so much.

Il est encore plus facile de juger de l'esprit d'un homme par ses questions que par ses réponses. (It is easier to judge the mind of a man by his questions rather than his answers) — Pierre-Marc-Gaston, duc de Lévis (1764-1830), Maximes et réflexions sur différents sujets de morale et de politique (Paris, 1808): Maxim xviii
Misattributed

Attributed quotes

Variant: Today is your day, your mountain is waiting. So get on your way.

Hawthorne and His Mosses (1850)
Context: It is better to fail in originality, than to succeed in imitation. He who has never failed somewhere, that man can not be great. Failure is the true test of greatness.
Context: It is better to fail in originality, than to succeed in imitation. He who has never failed somewhere, that man can not be great. Failure is the true test of greatness. And if it be said, that continual success is a proof that a man wisely knows his powers, — it is only to be added, that, in that case, he knows them to be small. Let us believe it, then, once for all, that there is no hope for us in these smooth pleasing writers that know their powers.

"Radio Power Will Revolutionize the World" in Modern Mechanics and Inventions (July 1934)
Context: The scientists from Franklin to Morse were clear thinkers and did not produce erroneous theories. The scientists of today think deeply instead of clearly. One must be sane to think clearly, but one can think deeply and be quite insane.

Variant: Life can only be understood going backward, but must be lived going forward.

Ch. IX : Outdoors and Indoors, p. 336; the final statement "quoted by Squire Bill Widener" as well as variants of it, are often misattributed to Roosevelt himself.
Variant: Do what you can, with what you have, where you are.
Attributed to Roosevelt in Conquering an Enemy Called Average (1996) by John L. Mason, Nugget # 8 : The Only Place to Start is Where You Are. <!-- The Military Quotation Book, Revised and Expanded: More than 1,200 of the Best Quotations About War, Leadership, Courage, Victory, and Defeat (2002) by James Charlton -->
Variant: Do what you can, with what you've got, where you are.
Context: There are many kinds of success in life worth having. It is exceedingly interesting and attractive to be a successful business man, or railroad man, or farmer, or a successful lawyer or doctor; or a writer, or a President, or a ranchman, or the colonel of a fighting regiment, or to kill grizzly bears and lions. But for unflagging interest and enjoyment, a household of children, if things go reasonably well, certainly makes all other forms of success and achievement lose their importance by comparison. It may be true that he travels farthest who travels alone; but the goal thus reached is not worth reaching. And as for a life deliberately devoted to pleasure as an end — why, the greatest happiness is the happiness that comes as a by-product of striving to do what must be done, even though sorrow is met in the doing. There is a bit of homely philosophy, quoted by Squire Bill Widener, of Widener's Valley, Virginia, which sums up one's duty in life: "Do what you can, with what you've got, where you are."

This Business of Living (1935-1950)

Quote attributed to Picasso in TIME, October 4, 1976, Modern Living: Ozmosis in Central Park http://quoteinvestigator.com/2015/03/07/child-art/ http://content.time.com/time/magazine/article/0,9171,918412,00.html
Disputed
Variant: All children are artists. The problem is how to remain an artist once he grows up.

Variant: The whole problem with the world is that fools and fanatics are always so certain of themselves, and wiser people so full of doubts.

Source: Pygmalion

Foreword (January 1960)
You Learn by Living (1960)

From a 1982 interview with Boston Globe journalist Marian Christy. Christy, Marian. "Winning according to Schwarzenegger." https://secure.pqarchiver.com/boston/doc/294151457.html Boston Globe: Boston, MA. 9 May 1982: p 51. Accessed 25 Jun 2016.
1980s
Context: Strength does not come from winning. Your struggles develop your strengths. When you go through hardships and decide not to surrender, that is strength. When you make an impasse passable, that is strength. But you must have ego, the kind of ego which makes you think of yourself in terms of superlatives. You must want to be the greatest. We are all starved for compliments. So we do things that get positive feedback.

Source: Journals of Ralph Waldo Emerson, with Annotations - 1841-1844

Laozi in the Tao Te Ching, Chapter 64
Misattributed, Chinese

Variant: You build on failure. You use it as a stepping sone. Close the door on the past. You don't try to forget the mistakes, but you don't dwell on it. You don't let it have any of your energy, or any of your time, or any of your space.

As quoted in Meditations for Women Who Do Too (1991) by Anne Wilson Schaef

Source: The Diary of a Young Girl