- The Eritrean War of Independence officially begins with the shooting of the Ethiopian police by Hamid Idris Awate.
- First meeting held of the Non-Aligned Movement. The Soviet Union resumes nuclear testing, escalating fears over the ongoing Berlin crisis.
September 7 - Tom and Jerry make a return with their first episode since 1957, Switchin' Kitten. The new creator, Gene Deitch makes 12 more Tom and Jerry episodes until 1962.
September 10 - During the F1 Italian Grand Prix on the circuit of Monza, German Wolfgang Von Trips, driving a Ferrari, crashes into a stand, killing 14 spectators and himself.
September 14 - The new military government of Turkey sentences 15 members of the previous government to death.
- The Focolare Movement opens its first North American center in New York.
September 17 - Military rulers in Turkey hang former prime minister Adnan Menderes.
September 18 - United Nations Secretary-General Dag Hammarskjöld dies in an air crash en route to Katanga, Congo.
September 21 - In France, the OAS slips an anti-de Gaulle message into TV programming.
September 24 - The old Deutsche Opernhaus in the Berlin neighborhood of Charlottenburg is returned to its newly rebuilt house as the Deutsche Oper Berlin.
- In the U.S., the Walt Disney anthology television series, renamed Walt Disney's Wonderful World of Color, moves from ABC to NBC after seven years on the air, and begins telecasting its programs in color for the first time. Years later, after Disney's death, the still-on-the-air program will be renamed The Wonderful World of Disney.
September 28 - A military coup in Damascus, Syria effectively ends the United Arab Republic, the union between Egypt and Syria.
September 30 - Organization for Economic Cooperation and Development (OECD) formed to replace the Organization for European Economic Co-operation (OEEC). (source: Wikipedia)