June 3: Singapore becomes a self-governing crown colony of Britain with Lee Kuan Yew as Prime Minister.
June 5: A new government of the State of Singapore is sworn in by Sir William Goode. Two former ministers are re-elected to the Legislative Assembly.
June 8: The USS Barbero and United States Postal Service attempt the delivery of mail via Missile Mail.
June 9: The USS George Washington is launched as the first submarine to carry ballistic missiles.
June 14: Disneyland Monorail System, the first daily operating monorail system in the Western Hemisphere, opens to the public in Anaheim, California. - A 3-front revolutionary invasion by air and sea takes place in the Dominican Republic, consisting of exiles aided by Fidel Castro and the Venezuelan government, whose objective is to overthrow dictator Rafael Leonidas Trujillo. Within a few days most are captured and executed. Only four are released by the government. Trujillo is killed less than two years later by men partly inspired by the deaths of the 1959 revolutionaries.
June 18: The film The Nun's Story, based on the best-selling novel, is released. Audrey Hepburn stars as the title character; she later says that this is her favorite film role. The film is a box-office hit, and is nominated for several Oscars.
June 23: Sean Lemass becomes the third Taoiseach of Ireland. - Convicted Manhattan Project spy Klaus Fuchs is released after only nine years in a British prison and allowed to emigrate to Dresden, East Germany where he resumes a scientific career.
June 25: A KH-1 Corona, believed to be the first operational spy satellite, is launched as science mission "Discoverer 4" from Vandenberg Air Force Base aboard a Thor-Agena rocket.
June 26: Elizabeth II (Queen of Canada) and U.S. President Dwight Eisenhower open the Saint Lawrence Seaway. - Darby O'Gill and the Little People, a film based on H.T. Kavanagh's short stories, is released in the U.S. by the Walt Disney Company after a world premiere in Ireland.
June 30: Twenty-one students are killed and more than a hundred injured when an American North American F-100 Super Sabre jet crashes into Miamori Elementary School on the island of Okinawa. The pilot ejected before the plane struck the school. (source: Wikipedia)