- Jan 1 European Economic Community, better known as the European Common Market starts operation
- Mar 27 Nikita Khrushchev becomes Soviet Premier as well as First Secretary of the Communist Party
- May 23 Mao Zedong starts the "Great Leap Forward" movement in China
- Aug 1 US atomic submarine USS Nautilus begins 1st transit of North Pole "operation Sunshine"
- Sep 12 US Supreme Court orders the all-white Central High School in Little Rock, Arkansas to integrate
- Dec 19 1st radio broadcast from space, US President Dwight D. Eisenhower Christmas message "to all mankind, America's wish for peace on Earth and goodwill to men everywhere"
- Dec 31 Cuban dictator Fulgencio Batista tells his Cabinet he is fleeing the country
- Mar 11 Charles Van Doren finally loses on US TV game show "Twenty-One" after winning $129,000 - later revealed to be fixed
- May 8 "Dracula" film starring Christopher Lee as the eponymous vampire, directed by Terence Fisher is the first Hammar Horror film released
- May 9 "Vertigo", American film noir psychological thriller directed by Alfred Hitchock, starring Jimmy Stewart and Kim Novak, is released
- Sep 5 1st color video recording on magnetic tape presented, Charlotte, North Carolina
- Jun 28 US Open Women's Golf, Forest Lake CC: Mickey Wright wins 1st of 4 Open titles by 5 from Louise Suggs; 1st player to win Open & LPGA in same year
- Jun 29 FIFA World Cup Final: Vavá & Pelé each score 2 goals as Brazil beats Sweden 5-2 in Stockholm, Sweden
- Dec 28 "The Greatest Game Ever Played", Baltimore Colts beat New York Giants 23-17 in the first every sudden-death overtime game in NFL history (17 future members of the Pro Football Hall of Fame were involved in the game)
Project SCORE, world’s first communications satellite launched from Cape Canaveral
On December 18, 1958