March 6 - Constantine II becomes King of Greece, upon the death of his father King Paul. American boxer Cassius Clay announces the change of his name to Muhammad Ali.

March 18 – Approximately 50 Moroccan students break into the embassy of Morocco in the Soviet Union and stage an all-day sit-in protesting against sentencing of eleven people to death for the alleged assassination attempt of King Hassan II of Morocco.

March 20 – The first United Nations Conference on Trade and Development takes place (lasts until June 6).

March 20 – The precursor of the European Space Agency, ESRO (European Space Research Organization) is established per an agreement signed on June 14, 1962.

March 21 – Non ho l'età (music by Nicola Salerno, text by Mario Panzeri), sung by Gigliola Cinquetti, wins the Eurovision Song Contest 1964 (staged in Copenhagen) for Italy.

March 27 - The Great Alaskan earthquake, the second-most powerful known (and the most powerful earthquake recorded in North American history) at a magnitude of 9.2, strikes Southcentral Alaska, killing 125 people and inflicting massive damage to the city of Anchorage.

March 28 – King Saud of Saudi Arabia abdicates. His brother, Prince Faisal, does not officially assume the throne until November.

March 31 – The military overthrows Brazilian President João Goulart in a coup, starting 21 years of dictatorship in Brazil, lasting until 1985. (source: Wikipedia)