1851 (MDCCCLI) was a common year starting on Wednesday (dominical letter E) of the Gregorian calendar and a common year starting on Monday (dominical letter G) of the Julian calendar, the 1851st year of the Common Era (CE) and Anno Domini (AD) designations, the 851st year of the 2nd millennium, the 51st year of the 19th century, and the 2nd year of the 1850s decade. Note that the Julian day for 1851 is 12 calendar days difference, which continued to be used from 1582 until the complete conversion of the Gregorian calendar was entirely done in 1929.
- January 11 – Hong Xiuquan officially begins the Taiping Rebellion.
- January 15 – Christian Female College, modern-day Columbia College, receives its charter from the Missouri General Assembly.
- January 23 – The flip of a coin, subsequently named Portland Penny, determines whether a new city in the Oregon Territory is named after Boston, Massachusetts, or Portland, Maine, with Portland winning.
- January 28 – Northwestern University is founded in Illinois.
- February 6 – Black Thursday in Australia: Bushfires sweep across the state of Victoria, burning about a quarter of its area.
- February 12 – Edward Hargraves claims to have found gold in Australia.
- February 15 – In Boston, Massachusetts, members of the anti-slavery Boston Vigilance Committee rescue fugitive slave Shadrach Minkins from a courtroom following his arrest by U.S. marshals.
- March 1 – Victor Hugo uses the phrase United States of Europe in a speech to the French National Assembly.
- March 11 – Giuseppe Verdi's opera Rigoletto is first performed at La Fenice in Venice.
- March 27 – The first white men reportedly see Yosemite Valley.
- March 30 – A population census is taken in the United Kingdom. The population reaches 21 million. 6.3 million live in cities of 20,000 or more in England and Wales and cities of 20,000 or more account for 35% of the total English population.
- April 9 – San Luis, the oldest permanent settlement in the state of Colorado, is founded by settlers from Taos, New Mexico.
- April 20 – Ramón Castilla loses power in Peru.
- April 21 – John Stuart Mill marries Harriet Taylor.
- April 28 – Santa Clara College is chartered in Santa Clara, California.
- May 1 – The Great Exhibition of the Works of Industry of All Nations in the Crystal Palace, Hyde Park, London is opened by Queen Victoria (it runs until October 18).
- May 15
- Mid-May to mid-July – Great Flood of 1851: extensive flooding across the Midwestern United States. The town of Des Moines is virtually washed away, and many rainfall records hold for 160 years.
- June 21 – The Immortal Game, a famous chess match, is played between Adolf Anderssen and Lionel Kieseritzky during a break in the first international tournament, held in London.
- July 1
- July 10 – The University of the Pacific is chartered as California Wesleyan College in Santa Clara, California.
- July 29 – Annibale de Gasparis, in Naples, Italy discovers asteroid 15 Eunomia.
- August 1 – Virginia closes its Reform Constitutional Convention deciding that all white men have the right to vote.
- August 22 – The yacht America wins the first America's Cup race, off the coast of England.
- September 15 – Saint Joseph's University is founded in Philadelphia.
- September 18 – The New York Times is founded.
- September 30 – The HSwMS Eugenie leaves from Karlskrona, Sweden to begin its voyage as the first Swedish Royal Navy vessel to circumnavigate the world.
- October – The Reuters news service is founded.
- October 15 – The City of Winona, Minnesota is founded.
- October 18 – The Great Exhibition in London is closed.
- October 24 – Ariel and Umbriel, moons of Uranus, are discovered by William Lassell.
- November 13
- November 14 – Herman Melville's novel Moby-Dick; or The Whale is published in the U.S. by Harper & Brothers, New York, after being first published on October 18 in London by Richard Bentley, in 3 volumes as The Whale.
- November 26–27 – Bombardment of Salé in Morocco by French naval forces in retaliation for looting of a French cargo ship.
- December 2 – French coup of 1851: In what amounts to a coup, Louis Napoleon, president of France, dissolves the French National Assembly and declares a new constitution to extend his term. A year later he declares himself as Emperor Napoleon III, ending the Second Republic.
- December 6 – The trial of Hélène Jégado begins; she is eventually sentenced to death and executed by guillotine.
- December 9 – The first YMCA in North America is established in Montreal.
- December 24 – The Library of Congress in Washington, D.C., burns.
- December 26–27 – A Royal Navy warship bombards Lagos Island; Oba Kosoko is wounded and flees to Epe.
- December 31 – The 1851 Chilean Revolution ends after the rebel defeat at the Battle of Loncomilla.
- St. Paul's College, Hong Kong is founded.
- Western Union is founded as the New York and Mississippi Valley Printing Telegraph Company.
- January 17 – A. B. Frost, American illustrator (d. 1928)
- January 19
- February 13 – Joseph B. Murdock, United States Navy admiral and New Hampshire politician (d. 1931)
- February 15 – Antero Rubín, Spanish general and politician (d. 1935)
- March 14 – John Sebastian Little, American politician and congressman (d. 1916)
- March 18
- March 19
- March 27 – Vincent d'Indy, French composer and teacher (d. 1931)
- March 28 – Bernardino Machado, Portuguese President (d. 1944)
- April 1 – Bruno von Mudra, German general (d. 1931)
- April 6 – Guillaume Bigourdan, French astronomer (d. 1932)
- April 13 – Robert Abbe, American surgeon (d. 1928)
- April 15 – Auguste Dubail, French general (d. 1934)
- April 17 – Madre Teresa Nuzzo, foundress of the Daughters of the Sacred Heart (d. 1923)
- April 20 – Young Tom Morris, Scottish golfer (d. 1875)
- April 21 – Charles Barrois, French geologist (d. 1939)
- May 6 – Aristide Bruant, French cabaret singer and comedian (d. 1925)
- May 7 – Adolf von Harnack, German Lutheran theologian and church historian (d. 1930)
- May 20 – Emile Berliner, telephone and recording pioneer (d. 1929)
- May 21 – Léon Bourgeois, French statesman, recipient of the Nobel Peace Prize (d. 1925)
- June 7 – Ture Malmgren, Swedish journalist and politician (d. 1922)
- June 12 – Sir Oliver Lodge, British physicist (d. 1940)
- June 13 – Anton Haus, Austro-Hungarian admiral (d. 1917)
- June 21 – Frederick Green (footballer), English Footballer (d. 1928)
- June 16 – Georg Jellinek, German legal philosopher (d. 1911)
- July 8 – Arthur Evans, British archaeologist (d. 1941)
- July 15 – Eduardo Gutiérrez, Argentinian author (d. 1889)
- July 20 – Arnold Pick, Czechoslovakian neurologist and psychiatrist (d. 1924)
- July 24 – Friedrich Schottky, German mathematician (d. 1935)
- August 14 – Doc Holliday, American gambler and gunfighter (d. 1887)
- September 1 – Carl Kellner (mystic), German mystic (d. 1905)
- September 7 – David King Udall, American politician (d. 1938)
- September 13 – Walter Reed, American army physician and bacteriologist (d. 1902)
- September 14 – H. E. Beunke, Dutch writer (d. 1925)
- September 16 – Eduard Reuss, German composer and music biographer (d. 1911)
- September 29 – Hardwicke Rawnsley, English clergyman, poet, writer of hymns and conservationist (d. 1920)
- October 2 – Ferdinand Foch, French commander of Allied forces in World War I (d. 1929)
- October 20 – George Gandy, American entrepreneur (d. 1946)
- November 10 – Richard Armstedt, German historian (d. 1931)
- November 16 – William Elbridge Sewell, American naval officer and Governor of Guam (d. 1904)
- November 27 – Friedrich Sixt von Armin, German general (d. 1936)
- December 10 – Melvil Dewey, American librarian, inventor of Dewey Decimal Classification (d. 1931)
- December 20 – Dora Montefiore, English suffragist and socialist (d. 1933)
- December 24 – Noël Édouard, vicomte de Curières de Castelnau, French general (d. 1944)
- December 30 – Asa Griggs Candler, American businessman and politician (d. 1929)
- January 10 – Karl Freiherr von Müffling, Prussian field marshal (b. 1775)
- January 19 – Esteban Echeverría, Argentine poet and writer (b. 1805)
- January 21 – Albert Lortzing, German composer (b. 1801)
- January 23 – Archibald Primrose, Lord Dalmeny, Scottish politician (b. 1809)
- January 27 – John James Audubon, French-American naturalist and illustrator (b. 1785)
- January 31 – David Spangler Kaufman, Congressman from Texas (b. 1813)
- February 1 – Mary Shelley, English author (b. 1797)
- February 3 – Benjamin Williams Crowninshield, Congressman from Massachusetts secretary of U.S. Navy (b. 1772)
- February 18 – Carl Gustav Jacob Jacobi, German mathematician (b. 1804)
- February 23 – Joanna Baillie, Scottish poet and dramatist (b. 1762)
- February 28 – Guillaume Dode de la Brunerie, Marshal of France (b. 1775)
- March 9 – Hans Christian Ørsted, Danish scientist (b. 1777)
- May 13 – Princess Augusta of Bavaria, Duchess of Leuchtenberg (b. 1788)
- May 22 – Mordecai Manuel Noah, American writer, journalist (b. 1785)
- July 10 – Louis Daguerre, French artist and chemist (b. 1787)
- July 17 – Roger Sheaffe, British General
- August 8 – James Broadwood, piano manufacturer (b. 1772)
- August 24 – James McDowell, American politician (b. 1795)
- September 10 – Thomas Hopkins Gallaudet, American educator (b. 1787)
- September 11 – Sylvester Graham, American nutritionist and inventor (b. 1794)
- September 14 – James Fenimore Cooper, American writer (b. 1789)
- October 4 – Manuel de Godoy, Spanish statesman (b. 1767)
- October 19 – Marie Thérèse of France (b. 1778)
- October 31 – Petar II Petrović-Njegoš, Montenegrin statesman, religious leader and poet (b. 1813)
- November 26 – Jean-de-Dieu Soult, French marshal and politician (b. 1769)
- December 19