January 21 – Peter I Island in the Antarctic first sighted by Fabian Gottlieb von Bellingshausen.
January 28 – Alexander Island, the largest in Antarctica, is first discovered by Fabian Gottlieb von Bellingshausen.
February 9 – Columbian College of the District of Columbia is chartered by President Monroe.
March 4 – James Monroe begins his second term as President of the United States.
March 5 – President James Monroe is sworn in for his second term.
March 25 (O.S.)/April 6 (N.S.) – Metropolitan bishop Germanos of Patras raises the revolutionary flag of Greece at the Monastery of Agia Lavra, symbolically marking the beginning of the Greek War of Independence against the Ottoman Empire; later celebrated as Greece's traditional Independence Day.
April 10 – Ecumenical Patriarch Gregory V of Constantinople is blamed by the Ottoman government for being unable to suppress Greek independence and is hanged outside the main gate of the Patriarchal Cathedral immediately after the celebration of Easter.
May 5 – Emperor Napoleon dies in exile on Saint Helena of stomach cancer.
May 26 – Establishment of the Peloponnesian Senate by the Greek rebels.
June 14 – King Badi VII of Sennar surrenders his throne and realm to Ismail Pasha, general of the Ottoman Empire, ending the existence of that Sudanese kingdom.
June 19 – The Filiki Eteria are decisively defeated by the Ottomans at Drăgășani (in Wallachia).
June 24 – Battle of Carabobo: Simón Bolívar wins Venezuela's independence from Spain.
June 27 – The New Hampton School is founded in the United States state of New Hampshire.
July 10 – The United States takes possession of its newly bought territory of Florida from Spain.
July 19 – George IV is crowned king of the United Kingdom of Great Britain and Ireland.
July 28 – Peru declares independence from Spain.
August 10 – Missouri is admitted as the 24th U.S. state (see History of Missouri).
August 19 – Navarino massacre: Greek rebels massacre 3,000 inhabitants of the city of Navarino.
August 21 – Jarvis Island is discovered by the crew of the Eliza Frances.
August 24 – Treaty of Córdoba signed in Córdoba, Veracruz, Mexico, ratifying the Plan of Iguala of February 24 for Mexico's independence from Spain and, although not recognised by the latter, effectively concludes the Mexican War of Independence.
Chilean general José Miguel Carrera is executed by an Argentinian military tribunal in the city of Mendoza.
The Ukase of 1821: Russia proclaims territorial sovereignty over Northwestern North America, modern-day Alaska.
September 7 – The Republic of Gran Colombia (a federation covering much of present-day Venezuela, Colombia, Panama, and Ecuador) is established, with Simón Bolívar as the founding President and Francisco de Paula Santander as vice president.
September 15 – Guatemala, El Salvador, Honduras, Nicaragua and Costa Rica gain independence from Spain by the Act of Independence of Central America. On October 29, the newly independent First Mexican Empire proposes that Guatemala should merge with it.
September 18 – Amherst College is founded in Massachusetts.
September 23 – Greek War of Independence: Siege of Tripolitsa ends when Greek rebels capture the city of Tripoli, Greece.
September 27 – The Army of the Three Guarantees enters Mexico City and the following day the Declaration of Independence of the Mexican Empire from Spain is proclaimed, following the Mexican War of Independence.
November 16 – American Old West: The Santa Fe Trail is first used by William Becknell.
November 28 – Panama declares independence from Spain, joining Gran Colombia.
December 1 – The Dominican Republic declares independence from Spain (see History of the Dominican Republic). It would be invaded by Haiti in 1822.
December 6 – The South Orkney Islands are discovered by George Powell and Nathaniel Palmer.
December 15 – The world's first geographical society, the Société de géographie, is established in Paris.
December 19 – The Eyjafjallajökull volcano in Iceland begins to erupt.
High-quality cotton is introduced in Egypt.
James Longstreet, American Confederate general (d. 1904)
W. H. L. Wallace, American Civil War general (d. 1862)
January 16 – John C. Breckinridge, the 14th Vice President of the United States from 1857 to 1861 and Confederate Secretary of State in 1865 (d. 1875).
February 3 – Elizabeth Blackwell, first American female physician (d. 1910).
Hermann Allmers, writer (d. 1902)
Auguste Edouard Mariette, French Egyptologist (d. 1881)
February 17 – Lola Montez, Irish Spanish dancer and royal mistress (d. 1861)
February 19 – August Schleicher, German linguist (d. 1868)
March 1 – Joseph Hubert Reinkens, German Old Catholic bishop (d. 1896)
March 9 – John Watts de Peyster, American author, philanthropist, and soldier (d. 1907)
March 12 – Sir John Abbott, 3rd Prime Minister of Canada (d. 1893)
March 15 – William Milligan, Scottish theologian (d. 1892)
April 1 – Princess Anka Obrenović, Serbian princess (d. 1868)
April 3 – Fr. Thomas Pelham Dale English mystic (d. 1892)
April 9 – Charles Baudelaire, French poet and writer (d. 1867)
May 6 – Edmund Colhoun, American admiral (d. 1897)
Emilie Hammarskjöld, Swedish-American musician (d. 1854)
May 8 – William Henry Vanderbilt, American entrepreneur (d. 1885)
May 16 – Pafnuty Chebyshev, Russian mathematician (d. 1894)
May 17 – Sebastian Kneipp, German naturopath (d. 1897)
June 16 – Old Tom Morris, Scottish golfer (d. 1908)
June 26 – Bartolomé Mitre, Argentine statesman, military figure, and author, sixth President of Argentina (d. 1906)
July 1 – Anatole Jean-Baptiste Antoine de Barthélemy, French archaeologist (d. 1904)
July 2 – Charles Tupper, 6th Prime Minister of Canada (d. 1915)
George Cavendish-Bentinck, British Conservative politician (d. 1891)
Adolphus Frederick Alexander Woodford, British parson (d. 1887)
July 13 – Nathan Bedford Forrest, American Confederate Civil War General, first Grand Wizard of the Ku Klux Klan (d. 1877)
July 16 – Mary Baker Eddy, American founder of Christian Science (d. 1910)
July 17 – Friedrich Engelhorn, German industrialist and founder of BASF (d. 1902)
July 18 – Pauline Viardot, French mezzo-soprano and composer (d. 1910)
July 24 – William Poole, infamous member of New York City's Bowery Boys gang (d. 1855)
July 27 – George H. Cooper, United States Navy admiral (d. 1891)
August 10 – Jay Cooke, American financier (d. 1905)
August 21 – Louis Vuitton, French fashion designer (d. 1892)
August 31 – Hermann von Helmholtz, German physician and physicist (d. 1894)
September 21 – Andrei Alexandrovich Popov, Russian admiral (d. 1898)
September 28 – Jonathan Clarkson Gibbs, African-American minister and politician (d. 1874)
October 13 – Rudolf Virchow, German physician, pathologist, biologist, and politician (d. 1902)
October 20 – Eufrosina Popescu, Romanian actress (d. 1900)
November 11 – Fyodor Dostoyevsky, Russian writer (d. 1881)
November 30 – Frederick Temple, Archbishop of Canterbury (d. 1902)
December 1 – John M. B. Clitz, American admiral (d. 1897)
December 12 – Gustave Flaubert, French writer (d. 1880)
December 22 – Junius Brutus Booth, Jr., American actor and theatre manager (d. 1883)
December 24 – Gabriel García Moreno, former President of Ecuador (d. 1875)
December 25 – Clara Barton, first president of American Red Cross (d. 1912)
Giuseppe Bonavia, Maltese architect (d. 1885)
January 4 – Elizabeth Ann Seton, American saint (b. 1774)
January 5 – Carlo Porta, Milanese poet (b. 1775)
January 19 – Alexandru Suţu, prince of Moldavia (b. 1758)
February 23 – John Keats, British poet (b. 1795)
March 4 – Princess Elizabeth of Clarence, daughter of William, Duke of Clarence (later King William IV) (b. 1820)
March 13 – John Hunter, second Governor of New South Wales (b. 1737)
April 10 – Patriarch Gregory V of Constantinople (b. 1746)
May 5 – Napoleon Bonaparte (b. 1769)
May 19 – Camille Jordan, French politician (b. 1771)
June 7 – Tudor Vladimirescu, Wallachian rebellion-leader (b. c. 1780)
June 17 – Martín Miguel de Güemes, Argentine military leader (b. 1785)
June 30 – José Fernando de Abascal y Sousa, viceroy of Peru (b. 1743)
July 4 – Richard Cosway, English artist (b. 1742)
August – Dorothea von Medem, Latvian diplomat and duchess of Courland (b. 1761)
August 24 – John Polidori, physician and writer (b. 1795) (suicide)
September 4 – José Miguel Carrera, Chilean general and founding father (b. 1785)
September 10 – Johann Dominicus Fiorillo, German painter and art historian (b. 1748)
September 14 – Heinrich Kuhl, German naturalist and zoologist (b. 1797)
October 4 – Marie Lachapelle, obstetrician (b. 1769)
October 8 – Juan O'Donojú, viceroy of New Spain (b. 1762)
October 11 – John Ross Key, commissioned officer in the Continental Army, judge, lawyer and the father of Francis Scott Key (b. 1754)
October 21 – Dorothea Ackermann, German actress (b. 1752)
November 8 – Jean Rapp, French general (b. 1771)
December 7 – Pōmare II, king of Tahiti (b. 1782)
December 12 – Phoebe Hessel, female soldier (b. 1713)
1821 (MDCCCXXI) was a common year starting on Monday (dominical letter G) of the Gregorian calendar and a common year starting on Saturday (dominical letter B) of the Julian calendar, the 1821st year of the Common Era (CE) and Anno Domini (AD) designations, the 821st year of the 2nd millennium, the 21st year of the 19th century, and the 2nd year of the 1820s decade. As of the start of 1821, the Gregorian calendar was 12 days ahead of the Julian calendar, which remained in localized use until 1923.