He formalized the theory of quantum mechanics, helped design the atomic bomb, and was central to the conception and development of the electronic computer (Mirowski 97). But as Mirowski argues, he also continued to critique neoclassical economics, and brought "cyborg science" to the discipline.
His early experiences with Marxism in Hungary (for three months in 1919) led him to a lifetime hatred of Marxism and Soviet communism. And coupled with his notions of noncooperative game theory, this leads him to pretty grim political stances, such as promoting a preemptive atomic strike against Russia in 1950: "If you say why not bomb them tomorrow, I say why not today? If you say at 5 o'clock, I say why not one o'clock?" At this point Russia had had the atomic bomb for less than a year. Since he didn't believe that political control of the atomic bomb was possible, he felt "at least initially...that world domination by the United States was the logical consequence of the atomic bomb."
I recall reading a terrific article by David Porush called I think "The Cyborg was a bomb" which argued that the cyborg era is crucially affected by the atomic bomb and its (sorry) fallout. And this again points to the way attitudes toward science and technology intersect with attitudes and practices of politics and economics. He truly felt that pure mathematics followed a laissez-faire kind of economics: not social planning or notions of applications for the math, but free exploration of mathematics, would ultimately lead to unknown uses. von Neumann argued that "Successes [in science] were largely due to forgetting completely about what one ultimately wanted, or whether one wanted anything ultimately...And I think it extremely instructive to watch the role of science in everyday life, and to note how the principle of laissez faire has led to strange and wonderful results." (quoted in Mirowski 101). Notice how this attitude - completely defensible in one sense (think of how much American science has been hurt by the short term vision of the government, cutting money for primary research and focusing on applications lo these many misguided years). And yet apply it to genetic engineering, or the family of nuclear weapons and energy, and you get a very different kind of laissez faire: one that "lets" the military adopt a super-imperial attitude toward the rest of the world, with all the paranoias and secrecy and terror this implies.
I read Mirowski and von Neumann and think of Dostoevsky, writing on the Grand Inquisitor, a piece that has always haunted me (for I truly believe it; I believe that many of the Popes were minimal on faith and maximal on control). Cybernetics, a la von Neumann, is about communication and/as control; the result is a 1950s whose leaders were like the Inquisitor, knowing that the pablum they were offering to the public to keep them happy was just that. The real existential political questions of all powerful leaders, especially those who control large militaries and other potent technologies, is whether it is ever possible to imagine a cooperative element to the "game" of political and military confrontation, control over resources and land.
Many have noted this element of the fable. The Wikipedia article on Grand Inquisitor mentions Tony Kushner's play Only We Who Guard The Mystery Shall Be Unhappy, Chomsky's reference in his book Necessary Illusions, and Huxley of course in Brave New World Revisited. But the one that I think is most connected to von Neumann type game theory is the X Files third season finale, "Talitha Cumi," where Cancer Man and Jeremiah Smith square off. I think X files captures the postwar paranoia and secrecy well.
One last comment here on von Neumann and the fifties: if it is true that his influence lies heavily on modern economics and on modern computing, it is worth noting this influence includes a legacy thought system based on a game theory that may be toxic to any notion of cooperation among the human states/tribes for common survival.
PS most people read The Grand Inquisitor as a separate thought piece. In the original novel The Brothers Karamazov, the subsequent chapters more or less comprise "answers" to the questions about the existence of God and the nature of freedom and political control (the wiki article mentions this). What few recall is the chapter that precedes this one, which I was amazed and moved by when I first read the novel as a young man. It sets up a world in which all would be well, as long as one child could be tortured. This inclusion of torture (Dostoevski himself was tortured by the Czar's police as a dangerous liberal) I think is crucial to the argument.