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Source: Robert Kennedy in His Own Words: The Unpublished Recollections of the Kennedy Years