- January 15 - University of Notre Dame receives its charter from Indiana.
- February 27 - The Dominican Republic gains independence from Haiti.
- February 28 - A gun on the USS Princeton explodes while the boat is on a Potomac River cruise, killing two United States Cabinet members and several others.
- May 23 - Persian Prophet The Báb announces His revelation, founding Bábism.
- May 24 - First electrical telegram sent by Samuel Morse from Baltimore, Maryland to Washington, D.C., saying "What hath God wrought?".
- June 6 - George Williams founds the Young Men's Christian Association in London, England.
- June 15 - Charles Goodyear receives a patent for vulcanization, a process to strengthen rubber.
- June 27 - Joseph Smith, Jr. is murdered with his brother Hyrum in Carthage Jail, Carthage, Illinois.
- July 3 - The last pair of Great Auks is killed.
- August 8 - During a meeting held in Nauvoo, the Quorum of Twelve, headed by Brigham Young, is created as the leading body of the Mormon Church.
- October 22 - Date predicted by the Millerites for the Second Coming of Jesus Christ; leads to the Great Disappointment.
- November - James K. Polk defeats Henry Clay in the U.S. presidential election
- November 6 - The Dominican Republic gains its independence from Spain.
- February 17 - Aaron Montgomery Ward, department store founder (d. 1913)
- February 20 - Ludwig Boltzmann, Austrian physicist
- February 20 - Joshua Slocum, seaman and adventurer (d. 1909)
- February 21 - Charles-Marie Widor, organist and composer
- March 10 - Pablo de Sarasate, violinist (d. 1908)
- March 18 - Nikolai Rimsky-Korsakov, composer (d. 1908)
- March 30 - Paul Verlaine, lyric poet (d. 1896)
- May 17 - Julius Wellhausen, German biblical scholar (d. 1918)
- May 19 - Charlotte of Mecklenburg-Strelitz (d. 1818)
- May 21 - Henri Rousseau, artist (d. 1910)
- May 22 - Mary Cassatt, artist
- May 23 - `Abdu'l-Bahá, Persian religious leader
- July 11 - King Peter I of Serbia
- July 22 - William Archibald Spooner, British scholar and Anglican priest
- August 6 - Prince Alfred of the United Kingdom, later Duke of Edinburgh and Duke of Saxe-Coburg and Gotha, second son of Queen Victoria
- August 17 - Menelik II, Emperor of Ethiopia
- August 22 - George Washington DeLong, American naval officer/ill-fated explorer (d. 1881)
- October 15 - Friedrich Nietzsche, German philosopher
- October 22 - Louis Riel, Metis leader
- October 22 - Sarah Bernhardt, French actress
- November 2 - Mehmed V, Ottoman Sultan (d. 1918)
- November 23 - Karl Benz, German automotive pioneer
- December 1 - Alexandra of Denmark, later Queen Consort of King Edward VII
- December 8 - Émile Reynaud, French science teacher, responsible for the first animation films.