- Edward Jenner develops vaccination, using cowpox to protect against smallpox
- February 1 - The capital of Upper Canada is moved from Newark to York
- March 30 - Carl Gauss obtained conditions for the constructibility by ruler and compass of regular polygons and was able to announce that the regular 17-gon was constructible by ruler and compasses.
- May 10 - First Coalition: Napoleon I of France wins a decisive victory against Austrian forces at Lodi bridge over the River Adda in Italy. The Austrians lose some 2,000 men.
- May 14 - Edward Jenner administers the first smallpox vaccination.
- June 1 - Tennessee is admitted as the 16th U.S. state.
- July 22 - Surveyors of the Connecticut Land Company name an area in Ohio "Cleveland" after Gen. Moses Cleaveland, the superintendent of the surveying party.
- September 8 - Napoleonic Wars: Battle of Bassano - French forces defeat Austrian troops at Bassano.
- November: John Adams defeats Thomas Jefferson in U.S. presidential election
- December 7 - U.S. Electoral College meets to elect John Adams president
- British government purchase a 40 acre site at Norman Cross the first purposely built prisoner of war camp in England at that time.
- February 22 - Lambert Adolphe Jacques Quetelet, mathematician (+ 1874)
- May 1 - Junius Brutus Booth, English actor.
- July 6 - Emperor Nicholas I of Russia
- August 25 - James Lick, California land baron (+ 1876)
- September 19 - Hartley Coleridge, British poet
- November 30 - Carl Loewe, composer