“Robert F. Kennedy used to say, 'Some men see things as they are and ask why. Others dream things that never were and ask why not?'; that outlook has become a far too common and destructive approach to interpreting the law”

Though Kennedy stated that he was quoting George Bernard Shaw when he said this, he is often thought to have originated the expression, which actually paraphrases a line delivered by the Serpent in Shaw's play Back To Methuselah: “You see things; and you say, ‘Why?’ But I dream things that never were; and I say, ‘Why not?’". This phrase was first used by his brother John F. Kennedy in 1963 (June 28th), during his visit to Ireland, in his address to the Irish Dail (Government): "George Bernard Shaw, speaking as an Irishman, summed up an approach to life, 'Other people, he said, see things and say why? But I dream things that never were and I say, why not?" ( Address on YouTube https://www.youtube.com/watch?v=8ADeazX9blw.). Robert's other brother Edward famously quoted it (paraphrasing it even further), to conclude his eulogy to his late brother after his assassination (8 June 1968): Some men see things as they are and say why? I dream things that never were and say why not? - (Eulogy in CBS news video) http://www.cbsnews.com/video/watch/?id=5268061n
Misattributed
Source: Robert Kennedy in His Own Words: The Unpublished Recollections of the Kennedy Years

The Serpent, in Pt. I : In the Beginning, Act I; this quote is sometimes misattributed to Robert F. Kennedy; it is often paraphrased slightly in a few different ways, including:
You see things as they are and ask, "Why?" I dream things as they never were and ask, "Why not?"
Variant: You see things; and you say "Why?" But I dream things that never were; and I say "Why not?
Source: 1920s, Back to Methuselah (1921)

Speech delivered to the Dail (Parliament of Ireland) (28 June 1963)
1963

Letter to Robert McAlmon (4 September 1943), published in The Selected Letters of William Carlos Williams (1957) edited by John C. Thirlwall, p. 217
General sources
Context: Why do we live? Most of us need the very thing we never ask for. We talk about revolution as if it was peanuts. What we need is some frank thinking and a few revolutions in our own guts; to hell with what most of the sons of bitches that I know and myself along with them if I don't take hold of myself and turn about when I need to — or go ahead further if that's the game.

Adverbs (2006), Particularly

Opening epigram
Finch (2009)

Source: The Sacred Depths of Nature (1998), p. 167
Context: We are, each one of us, ordained to live out our lives in the context of ultimate questions, such as:
Why is there anything at all, rather than nothing?
Where did the laws of physics come from?
Why does the universe seem so strange?
My response to such questions has been to articulate a covenant with Mystery. Others, of course, prefer to respond with answers, answers that often include a concept of god. These answers are by definition beliefs since they can neither be proven nor refuted. They may be gleaned from existing faith traditions or from personal search. God may be apprehended as a remote Author without present-day agency, or as an interested Presence with whom one can form a relationship, or as pantheistic — Inherent in All Things.
The opportunity to develop personal beliefs in response to questions of ultimacy, including the active decision to hold no Beliefs at all, is central to the human experience. The important part, I believe, is that the questions be openly encountered. To take the universe on — to ask Why Are Things As They Are? — is to generate the foundation for everything else.

Source: Pablo Picasso: Metamorphoses of the Human Form : Graphic Works, 1895-1972