- Birmingham riots, England
- January 25 - The British Parliament passes the Constitutional Act of 1791, splitting the old province of Quebec into Upper and Lower Canada
- March 3 - The United States Mint is created by the United States Congress.
- March 4 - Vermont is admitted as the 14th U.S. state.
- May 3 - Constitution of third May (first Polish constitution) proclaimed by Polish Sejm (Parliament)
- December 15 - The United States Bill of Rights is passed.
- 1791 in literature:
- 1791 in music
- January 15 - Franz Grillparzer, Austrian lyricist (&(+ 1872)
- February 21 - John Mercer, chemist and industrialist (+ 1866)
- April 27 - Samuel Morse, U.S. inventor
- December 26 - Charles Babbage, English mathematician and inventor of computing machines
- Michael Faraday - English scientist
- May 9 - Francis Hopkinson, American author and signer of the Declaration of Independence
- December 5: Wolfgang Amadeus Mozart - Austrian composer