“Putin is willing to poison bodies in the free world, not only minds. Why would he do this? Why would he call attention to his murderous ways now? Well, I’ll turn that around and ask instead, why wouldn’t he? Dictators don’t ask “Why,” they ask “Why not?””

As quoted in "Is Putin Popular?" https://www.nationalreview.com/2018/03/is-putin-popular-c/ (2018), by Jay Nordlinger, National Review
2010s

Source: The Irresistible Revolution (2006), p. 65

Adele Astaire op. cit.

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Source: Robert Kennedy in His Own Words: The Unpublished Recollections of the Kennedy Years

"A Man of the People", p. 106
Four Ways to Forgiveness (1995)

Quoted by Martin Buber in Tales of the Hassidim: The Early Masters, Shocken Books 1968, p. 141.

Source: The Rose That Grew from Concrete

In "Jack LaLanne dies at 96; spiritual father of U.S. fitness movement, LosAngeles Times"

Source: Bob Marley Talking