December 1 – Gustavo Díaz Ordaz takes office as President of Mexico.

December 3 - Police arrest about 800 students at the University of California, Berkeley, following their takeover of and massive sit-in at the Sproul Hall administration building. The sit-in most directly protested the U.C. Regents' decision to punish student activists for what many thought had been justified civil disobedience earlier in the conflict.

The Danish football club Brøndby IF is founded as a merger between the two local clubs Brøndbyøster Idrætsforening and Brøndbyvester Idrætsforening. The club wins the national championship Danish Superliga 10 times, and the Danish Cups six times, after joining the Danish top-flight football league in 1981.

December 5 – Australian Senate election, 1964: The Liberal/Country Coalition Government led by Prime Minister Robert Menzies hold their status quo, while the Labor Party led by Arthur Calwell lose one seat to the Democratic Labor Party, who hold the balance of power in the Senate alongside independent Reg Turnbull.

December 10 – Dr. Martin Luther King Jr. is awarded the Nobel Peace Prize in Oslo, Norway.

December 11 – Che Guevara addresses the United Nations General Assembly. A bazooka attack is launched at the Headquarters of the United Nations in New York City.

December 12 – Jamhuri Day: Kenya becomes a republic, with Jomo Kenyatta as its first President.

December 14 – Heart of Atlanta Motel v United States: The U.S. Supreme Court rules that, in accordance with the Civil Rights Act of 1964, establishments providing public accommodation must refrain from racial discrimination.

December 18 – The Christmas flood of 1964 begins in the United States, affecting the Pacific Northwest and some of Northern California. It will continue until January 7, resulting in 19 deaths, serious damage to buildings, roads and bridges, and the loss of 4,000 head of livestock.

December 21 – The General Dynamics F-111 Aardvark supersonic attack aircraft, developed for the U.S. Air Force, makes its first flight, at Carswell Air Force Base, Texas.

December 22 - A cyclone in the Palk Strait destroys the Indian town of Dhanushkodi, killing 1800 people. The Lockheed SR-71 Blackbird makes its first flight at Palmdale, California.

December 24 – The Brinks Hotel in Saigon, Vietnam, is bombed by the Viet Cong, resulting in the deaths of two US soldiers and injuries to a further 60 people, including civilians.

December 30 – The United Nations Conference on Trade and Development (UNCTAD) is established as a permanent organ of the UN General Assembly. (source: Wikipedia)