1821

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March 25 (April 6 in the Julian calendar): Germanos of Patras declares the independence of Greece from the Ottoman Empire to start the Greek War of Independence.

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Events

January–March

January 21 – Peter I Island in the Antarctic is first sighted, by Fabian Gottlieb von Bellingshausen.
January 26 – Congress of Laibach convenes to deal with outstanding international issues, particularly the outbreak of a revolution in southern Italy.
January 28 – Alexander Island, the largest in Antarctica, is first discovered by Fabian Gottlieb von Bellingshausen.
February 9 – Columbian College in the District of Columbia is chartered by President James Monroe (it becomes George Washington University).
February 10 – In Mexico, the Embrace of Acatempan takes place between Agustín de Iturbide and Vicente Guerrero, which seals the peace between the viceroyalty troops and the insurgents.
February 28 – Congress of Laibach formally comes to an end. However the leading participants remain as fresh uprisings break out in Northern Italy and Greece.<ref>Palmer, Alan. Alexander I: Tsar of War and Peace. Faber and Faber, 2011 p.416-17</ref>
March 7 – The Battle of Rieti is fought in Italy between intervening Austrian forces and Neapolitan rebels.<ref>Roberts, Warren. Rossini and Post-Napoleonic Europe. Boydell & Brewer, 2015. p.111</ref>
March 21 – Austrian forces under Johann Frimont enter Naples and restore the authority of Ferdinand I.

April–June

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 (according to oral tradition), symbolically marking the beginning of the Greek War of Independence against the Ottoman Empire; later celebrated as Greece's traditional Independence Day.
April 10 (O.S.)/April 22 (N.S.) – 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 Pascha.
May 5
- Emperor Napoleon dies in exile on Saint Helena of stomach cancer.
- The first edition of the Manchester Guardian newspaper (from 1959 simply The Guardian) is published in England.<ref>Template:Cite news</ref>
May 8 – Greek War of Independence: At the Battle of Gravia Inn, a 120-man Greek force led by Odysseas Androutsos repulses an Ottoman army of 8,000.
May 12 – Congress of Laibach finally ends having overseen the successful Austrian intervention in Italy. A planned Congress of Verona in 1822 is agreed as the next meeting.
June 14 – Egyptian conquest of Sudan (1820–1824): King Badi VII of Sennar surrenders his throne and realm without a fight to Ismail Pasha, general of the Ottoman Empire, ending the existence of the Funj Sultanate in Sudan.
June 7 (O.S.)/June 19 (N.S.) – Battle of Drăgășani, Wallachia: The Filiki Eteria are decisively defeated by the Ottomans.

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June 24: Battle of Carabobo

June 24 – Battle of Carabobo: Simón Bolívar wins Venezuela's independence from Spain.

July–September

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July 19: Coronation of George IV of the United Kingdom

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July 28: Proclamation of the Independence of Peru

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September 15: Declaration of Independence of Central America

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September 27: Entrance of the Army of the Three Guarantees to Mexico City

July 4 – Return of John VI from Brazil to Portugal who approves on that day the Bases da Constituição.
July 19 – George IV is crowned King of the United Kingdom of Great Britain and Ireland. His estranged wife, Caroline of Brunswick, is turned away from the ceremony.
July 28 – Argentine general José de San Martín declares the independence of Peru from the Spanish Empire.
August 10 – Missouri is admitted as the 24th U.S. state.
August 7 (O.S.)/August 19 (N.S.) – Navarino massacre: Greek rebels massacre 3,000 inhabitants of the city of Navarino.
August 21 – Jarvis Island is discovered in the Pacific by the crew of the Eliza Frances.
August 24 – The Treaty of Córdoba is 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.
August 30 – At the Congress of Cúcuta, 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 4 – Chilean general José Miguel Carrera is executed by an Argentinian military tribunal, in the city of Mendoza.
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 be annexed with it.
September 4 (O.S.)/September 16 (N.S.) – Ukase of 1821: Russia proclaims territorial sovereignty over Northwestern North America, modern-day Alaska.
September 18 – Amherst College is founded in Massachusetts.
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.

October–December

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October 5 (September 23 Greek calendar): The Siege of Tripolitsa by Greek rebels is followed by a massacre.

September 23 (O.S.)/October 5 (N.S.) – The Siege of Tripolitsa ends when Greek rebels capture the city of Tripoli, Greece; the massacre of 8,000 civilians follows. (Greek forces under the command of General Theodoros Kolokotronis have besieged the city for several months during the Greek War of Independence from Turkey and the Ottoman Empire.)<ref>Template:Cite book</ref><ref>Template:Cite book</ref>
October 8 (O.S.)/October 20 (N.S.) – Tsar Alexander I of Russia issues an imperial ukase guaranteeing freedom of commerce in Russia by merchants from Persia.<ref>"Commerce between Russia and Persia— Proposed Union of the Black Sea with the Atlantic". The Oriental Herald (November 1826) p. 285.</ref>
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 – History of the Dominican Republic: On the Caribbean island of Hispaniola, General José Núñez de Cáceres ends the España Boba era of Spanish rule in the Captaincy General of Santo Domingo by establishing the Republic of Spanish Haiti. It will last for three months before being invaded by Haiti.
December 6 – The South Orkney Islands are discovered by seal hunters George Powell and Nathaniel Palmer.<ref>Template:Cite book</ref><ref>Template:Cite encyclopedia</ref>
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.

Date unknown

The town of Al-Ubayyid, Sudan is established.
Widener University is founded in Wilmington, Delaware, as The Bullock School for Boys.

Births

January–June

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James Longstreet

January 1 – Francisco de Paula Milán Mexican officier of the Mexican Army (d. 1883)
January 2 – Catherine Huggins, British actor, singer, director and manager (d. 1887)
January 8
- James Longstreet, American Confederate general (d. 1904)
- W. H. L. Wallace, American Civil War general (d. 1862)
February 3 – Elizabeth Blackwell, first American female physician (d. 1910)
February 11 – Auguste Edouard Mariette, French Egyptologist (d. 1881)
February 17 – Lola Montez, Irish-Spanish dancer, royal mistress (d. 1861)
February 19
- Francis Preston Blair Jr., American politician, American Civil War officer (d. 1875)
- 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 31 – Henry Dunning Macleod, Scottish economist (d. 1902)
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, writer (d. 1867)<ref>Charles Baudelaire, Richard Howard. Les Fleurs Du Mal. David R. Godine Publisher, 1983, p.xxv. Template:ISBN, Template:ISBN.</ref>
April 12 – Beauchamp Seymour, British admiral (d. 1895)
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)
May 18 – Eduard von Pestel, Prussian military officer and German general (d. 1908)
May 24 – Juan Bautista Topete, Spanish admiral and politician (d. 1885)
June 2 – Ion C. Brătianu, 2-Time Prime Minister of Romania (d. 1891)
June 16 – Old Tom Morris, Scottish golfer (d. 1908)
June 26 – Bartolomé Mitre, Argentine statesman, military figure, and author, 6th President of Argentina (d. 1906)