January 3 - President Dwight D. Eisenhower announces that the United States has severed diplomatic and consular relations with Cuba.
- At the National Reactor Testing Station near Idaho Falls, Idaho, atomic reactor SL-1 explodes, killing 3 military technicians.
- Aero Flight 311 (Koivulahti air disaster): Douglas DC-3C OH-LCC of Finnish airline Aero crashes near Kvevlax (Koivulahti) on approach to Vaasa Airport in Finland killing all 25 on board, due to pilot error: an investigation finds that the captain and first officer were both exhausted for lack of sleep and had taken excessive alcohol at the time of the crash. It remains the deadliest air disaster to occur in the country.
January 5 - Italian sculptor Alfredo Fioravanti marches into the U.S. Consulate in Rome, and confesses that he was part of the team that forged the Etruscan terracotta warriors in the Metropolitan Museum of Art.
- Cemal Gürsel forms the new government of Turkey (25th government)
January 7 - Following a 4-day conference in Casablanca, 5 African chiefs of state announce plans for a NATO-type African organization to ensure common defense. The Charter of Casablanca involves the Casablanca Group: Morocco, the United Arab Republic, Ghana, Guinea, and Mali.
January 8 - In France, a referendum supports Charles de Gaulle's policies on independence for Algeria.
January 9 - British authorities announce that they have discovered a large Soviet spy ring in London.
January 17 - President Dwight Eisenhower gives his final State of the Union Address to Congress. In a Farewell Address the same day, he warns of the increasing power of a "military-industrial complex."
- Patrice Lumumba of Republic of Congo is assassinated.
January 20 - John F. Kennedy succeeds Dwight Eisenhower as the 35th President of the United States of America.
January 24 - B-52 Stratofortress, with two nuclear bombs, crashes near Goldsboro, North Carolina.
January 25 - In Washington, DC President John F. Kennedy delivers the first live presidential news conference. In it, he announces that the Soviet Union has freed the 2 surviving crewmen of a USAF RB-47 reconnaissance plane shot down by Soviet flyers over the Barents Sea July 1, 1960 (see RB-47H shot down).
- Acting to halt 'leftist excesses,' a junta composed of 2 army officers and 4 civilians takes over El Salvador, ousting another junta that had ruled for 3 months.
January 26 - President John F. Kennedy appoints Janet G. Travell to be his physician, the first woman to hold this appointment.
January 30 - President John F. Kennedy delivers his first State of the Union Address.
January 31 - Ham the Chimp, a 37-pound (17-kg) male, is rocketed into space aboard Mercury-Redstone 2, in a test of the Project Mercury capsule, designed to carry United States astronauts into space. (source: Wikipedia)