Most people know of President Kennedy's 1962 speech at Rice University challenging the nation to land a man on the Moon before the end of the decade. But fifty years ago today he gave a speech at the United Nations with a somewhat different message.
In what turned out to be his final address to the General Assembly of the United Nations, Kennedy raised the possibility of a joint US/USSR mission to the Moon:
Space offers no problems of sovereignty; by resolution of this Assembly, the members of the United Nations have foresworn any claim to territorial rights in outer space or on celestial bodies, and declared that international law and the United Nations Charter will apply. Why, therefore, should man's first flight to the moon be a matter of national competition? Why should the United States and the Soviet Union, in preparing for such expeditions, become involved in immense duplications of research, construction, and expenditure? Surely we should explore whether the scientists and astronauts of our two countries—indeed of all the world—cannot work together in the conquest of space, sending some day in this decade to the moon not the representatives of a single nation, but the representatives of all of our countries.
Given the state of the Cold War at the time, it's certainly questionable whether a joint expedition could have actually happened. But since Kennedy was assassinated two months later, we'll never know for sure.
The whole speech can be read here.