|Covid-19|January 11 – Michigan Territory is created.
February 15 – The Harmony Society is officially formed as a Christian community in Harmony, Pennsylvania.
March 1 – Justice Samuel Chase is acquitted of impeachment charges by the United States Senate.
March 4 – Thomas Jefferson is sworn in for a second term as President of the United States.
March 5 – The New Brunswick Legislature passes a bill to advance literacy in the province, which eventually leads to the creation of public education in what is now Canada.
April 7 – Beethoven's Symphony No. 3, Eroica, has its public premiere at the Theater an der Wien in Vienna under his baton.
April 27 – Battle of Derne: United States Marines and Berbers attack the Tripolitan city of Derna (the "Shores of Tripoli").
April 29 – Rutger Jan Schimmelpenninck is appointed as Grand Pensionary of the Batavian Republic by Napoleon.
May 26 – Napoleon is crowned King of Italy.
May 31–June 2 – Napoleonic Wars – Battle of Diamond Rock: A Franco-Spanish fleet captures the strategic island of Diamond Rock off Martinique in the West Indies from the British occupying force.
June 1 – Tuscan-born composer Luigi Boccherini is buried in St. Michael's Basilica, Madrid, after being found dead on May 28.
June 4 – The First Barbary War ends between Tripoli and the United States of America.
The first Trooping the Colour ceremony is held at the Horse Guards Parade in London.
Detroit burns to the ground; most of the city is destroyed.
June 13 – Lewis and Clark Expedition in the United States: Scouting ahead of the expedition, Meriwether Lewis and four companions sight the Great Falls of the Missouri River, confirming they are heading in the right direction.
July 9 – Muhammad Ali Pasha founds his dynasty in Egypt.
July 26 – An earthquake killed 5,573 people in Molise and Campania, Italy
October 14 – Napoleonic Wars: War of the Third Coalition, Ulm Campaign: Battle of Elchingen – An Austrian corps under Johann von Riesch is defeated by Marshal Ney near Elchingen in Bavaria.
October 16–19 – War of the Third Coalition, Ulm Campaign: Battle of Ulm – Austrian General Mack von Leiberich is forced to surrender his entire army to Napoleon after being surrounded.
October 21 – Napoleonic Wars: War of the Third Coalition – Battle of Trafalgar: British naval fleet led by Admiral Horatio Nelson defeats a combined French and Spanish fleet off the coast of Spain; however, Admiral Nelson is fatally shot.
November 7 – The Lewis and Clark Expedition arrives at the Pacific Ocean.
November 11 – Napoleonic Wars – Battle of Dürenstein: 8,000 French troops attempt to slow the retreat of a vastly superior Russian and Austrian force.
November 16 – Napoleonic Wars – Battle of Schöngrabern: Russian forces under Pyotr Bagration delay the pursuit by French troops under Joachim Murat.
November 20 – Beethoven's only opera Fidelio in its original form (known retrospectively as Leonore) is premiered at the Theater an der Wien in Vienna, which at this time is under French military occupation.
November 26 – The Pontcysyllte Aqueduct is opened in Wales; it is 1,007 ft (307 m) long and 126 ft (38 m) tall.
December 2 – Napoleonic Wars – Battle of Austerlitz: French troops under Napoleon decisively defeat a joint Russo-Austrian force.
December 26 – The Peace of Pressburg is signed between France and Austria.
King Anouvong becomes ruler of Vientiane.
Napoleon annuls the 10-day week of the French Republican Calendar with effect from 1 January 1806 (the day after 10 Nivôse an XIV); he also orders his soldiers to be vaccinated.
Sweden declares war on France.
The Horse Patrol, a mounted law enforcement force, is founded in London, England.
James Squire becomes the first person in Australia to cultivate Hops.
Old Man of the Mountain is first mentioned.
January 8 – Orson Hyde, American religious leader (d. 1878)
January 27 – Samuel Palmer, English artist (d. 1881)
February 13 – Peter Gustav Lejeune Dirichlet, German mathematician (d. 1859)
February 18 – Louis M. Goldsborough, United States Navy admiral (d. 1877)
March 3 – Jonas Furrer, first President of the Swiss Confederation (d. 1861)
March 23 – Sears Cook Walker, American mathematician and astronomer (d. 1853)
March 26 – Shirali Muslimov, World's longest lived person than Jeanne Calment (d. 1973)
April 2 – Hans Christian Andersen, Danish writer (d. 1875)
April 8 – Hugo von Mohl, German botanist (d. 1872)
April 22 – Benito de Soto, Galician pirate (d. 1830)
June 9 – José Trinidad Cabañas, Honduran General, President and National Hero (d. 1871)
June 22 – Giuseppe Mazzini Italian patriot, statesman, and writer (d. 1872)
July 5 – Robert FitzRoy, English meteorologist, captain and politician (d. 1865)
July 29 – Alexis de Tocqueville, French historian (d. 1859)
July 30 – Rudolf Wagner, German anatomist and pathologist (d. 1864)
August 4 – William Rowan Hamilton, Irish physicist (d. 1865)
September 19 – John Stevens Cabot Abbott, American historian, pastor, and pedagogical writer (d. 1877)
September 27 – George Müller, Prussian evangelist and founder of the Ashley Down orphanage in England (d. 1898)
November 14 – Fanny Mendelssohn, German composer and pianist (d. 1847)
November 28 – John Lloyd Stephens, American traveler, diplomat and Mayanist archaeologist (d. 1852)
December 2 – Cicero Price, American commodore (d. 1888)
December 10 – William Lloyd Garrison, American abolitionist (d. 1879)
December 22 – John Obadiah Westwood, English entomologist (d. 1893)
December 23 – Joseph Smith, founder of The Church of Jesus Christ of Latter Day Saints Church and Latter Day Saint movement (d. 1844)
December 31 – Jeanne Deroin, French socialist feminist (d. 1894)
Maiden of Ludmir, Jewish religious leader (d. 1888)
January 9 – Noble Wimberly Jones, American Continental Congressman (b. 1723)
January 18 – John Moore (archbishop of Canterbury) (b. 1730)
January 23 – Claude Chappe, French telecommunication pioneer (b. 1763)
February 20 – Justus Claproth, German jurist and inventor of the deinking process of recycled paper (b. 1728)
February 25 – Thomas Pownall, English colonial statesman (b. 1722)
March 4 – Jean-Baptiste Greuze, French painter (b. 1725)
May 7 – William Petty, 2nd Earl of Shelburne, Prime Minister of the United Kingdom (b. 1737)
May 9 – Friedrich Schiller, German playwright (b. 1759)
May 12 – Ferdinand von Hompesch zu Bolheim, 71st Grandmaster of the Order of Malta (b. 1744)
May 25 – William Paley, English philosopher (b. 1743)
May 28 – Luigi Boccherini, Tuscan-born composer (b. 1743)
June 19 – Louis-Jean-François Lagrenée, French painter (b. 1724)
August 3 – Christopher Anstey, English writer (b. 1724)
August 28 – Alexander Carlyle, Scottish church leader (b. 1722)
October 5 – Charles Cornwallis, 1st Marquess Cornwallis, British general (b. 1738)
October 5 – Eleonore Prochaska, German heroine soldier (b. 1785)
October 21 – Horatio Nelson, British admiral (mortally wounded in battle) (b. 1758)
December 16 – Saverio Cassar, Gozitan priest and rebel leader (b. 1746)
December 23 – Pehr Osbeck, Swedish explorer and naturalist (b. 1723)
December 23 – Geneviève Thiroux d'Arconville, French novelist, translator and chemist (b. 1720)
date unknown – Rafaela Herrera, Nicaraguan heroine (b. 1742)
1805 (MDCCCV) was a common year starting on Tuesday (dominical letter F) of the Gregorian calendar and a common year starting on Sunday (dominical letter A) of the Julian calendar, the 1805th year of the Common Era (CE) and Anno Domini (AD) designations, the 805th year of the 2nd millennium, the 5th year of the 19th century, and the 6th year of the 1800s decade. As of the start of 1805, the Gregorian calendar was 12 days ahead of the Julian calendar, which remained in localized use until 1923. After thirteen years the First French Empire abolished the French Republican Calendar in favour of the Gregorian calendar.