October 1 - Nigeria becomes independent from United Kingdom, and Nnamdi Azikiwe becomes its first native-born Governor General. - Cameroon declared independence from United Kingdom.

October 3 - Jãnio Quadros is elected the President of Brazil for a five-year term.

October 5 - White South Africans vote to make the country a republic.

October 7 - Nigeria becomes the 99th member of the United Nations.

October 12 - Cold War: Soviet premier Nikita Khrushchev pounds his shoe on a table at a meeting of the United Nations General Assembly, his way of protesting the discussion of the Soviet Union's policies toward Eastern Europe. - Otoya Yamaguchi assassinates Inejiro Asanuma, the chairman of the Japanese Socialist Party.

October 13 - The Pittsburgh Pirates won the 1960 World Series of baseball in Game 7, on a home run hit by Bill Mazeroski for a 10-9 victory over the New York Yankees. It was the first time in the history of the Series that a homer had won the championship.

October 14 - Presidential candidate John F. Kennedy first suggests the idea for the Peace Corps of the United States.

October 24 - A large rocket explodes on the launch pad at the Baikonur Cosmodrome, killing at least 90 people of the Soviet space program.

October 26 - Robert F. Kennedy telephones Coretta Scott King, the wife of Dr. Martin Luther King, Jr., and he also secures King's release from jail regarding a traffic violation in Atlanta, Georgia, U.S..

October 29 - In Louisville, Kentucky, Cassius Clay (later Muhammad Ali) wins his first professional boxing match.

October 30 - Dr. Michael Woodruff carries out the first successful kidney transplant in the United Kingdom, in Edinburgh, Scotland, at the Edinburgh Royal Infirmary. (source: Wikipedia)