Serial publication of Charles Dickens' novel Martin Chuzzlewit begins in London. In the July chapters, he lands his hero in the United States.
Publication of Edgar Allan Poe's Gothic short story "The Tell-Tale Heart" in a Philadelphia magazine.
The Quaker magazine The Friend is first published in London.
January 3 – Publication in China of Illustrated Treatise on the Maritime Kingdoms (海國圖志, Hǎiguó Túzhì) compiled by Wei Yuan and others, the first significant Chinese work on the West.
January 6 – Antarctic explorer James Clark Ross discovers Snow Hill Island.
January 20 – Honório Hermeto Carneiro Leão, Marquis of Paraná, becomes de facto first prime minister of the Empire of Brazil.
February 3 – Uruguayan Civil War: Argentina supports Oribe of Uruguay and begins a siege of Montevideo.
February 6 – The Virginia Minstrels perform the first minstrel show, at the Bowery Amphitheatre in New York City.
February 11 – Giuseppe Verdi's opera I Lombardi alla prima crociata premieres at La Scala in Milan.
February 14 – The event that inspired the Beatles song "Being for the Benefit of Mr. Kite!" is held in England.
February 25 – Lord George Paulet occupies the Kingdom of Hawaii in the name of Great Britain in the Paulet Affair (1843).
March 8 – The Danish government re-establishes the Althing in Iceland as an advisory body, by royal decree.
March 11–March 14 – Eta Carinae flares to become the second brightest star.
March 13 – Catawba County, North Carolina, is created and its first court held in Mathias Barringer Jr.'s house.
March 15 – Victoria, British Columbia, is founded by the Hudson's Bay Company as a trading post and fort.
March 16 – The city of Petrópolis is founded by the government of Brazil.
March 21 – The world does not end, contrary to the first prediction by American preacher William Miller.
March 24 – Battle of Hyderabad: The Bombay Army led by Major General Sir Charles Napier defeats the Talpur Emirs, securing Sindh as a Province of British India.
March 25 – Marc Isambard Brunel's Thames Tunnel, the first tunnel under the River Thames and the world's first bored underwater tunnel, is opened in London.
April – Eta Carinae is temporarily the second-brightest star in the night sky.
April 7 – The Indian Slavery Act, 1843 removes legal support for slavery within the territories of the East India Company
May 4 – Natal is proclaimed a British colony.
May 18 – The Disruption in Edinburgh of the Free Church of Scotland from the Church of Scotland.
May 22 – The first major wagon train headed for the American Northwest sets out with one thousand pioneers from Elm Grove, Missouri on the Oregon Trail.
May 23 – Chile takes possession of the Strait of Magellan.
June 6 – In Barbados, Samuel Jackman Prescod is the first non-white person elected to the House of Assembly.
June 17 – Wairau Affray in the South Island of New Zealand: An armed posse of British settlers sent to arrest Māori chief Te Rauparaha clash with members of his Ngāti Toa tribe, resulting in 26 deaths
June 21 – Edgar Allan Poe's short story "The Gold-Bug" begins serialization in American newspapers.
July 1 – Graduation from a class of 39 at the United States Military Academy, West Point, of Ulysses S. Grant (21st) and John J. Peck (8th).
July 19 – Isambard Kingdom Brunel's SS Great Britain is launched from Bristol; it will be the first iron-hulled, propeller-driven ship to cross the Atlantic Ocean.
July 25 – Père Antoine Désiré Mégret, a Capuchin missionary, purchases for $900 the land that will become Abbeville, Louisiana, a town founded by descendants of Acadians from Nova Scotia.
August 1 – Brazil becomes the second country, after Great Britain, to issue nationally valid postage stamps with the release of its "Bull's Eye" series.
August 15 – Tivoli Gardens, one of the oldest still intact amusement parks in the world, opens in Copenhagen, Denmark.
September – Ada Lovelace translates and expands Menabrea's notes on Charles Babbage's Analytical Engine, including an algorithm for calculating a sequence of Bernoulli numbers, regarded as the world's first computer program.
September 2 –The Economist newspaper is first published in London (preliminary issue dated August).
September 4 – The Emperor Dom Pedro II of Brazil marries Dona Teresa Cristina of the Two Sicilies in a state ceremony in Rio de Janeiro Cathedral.
September 15 (Sept. 3, O.S.) – Popular uprising in Athens, Greece, including citizens and military captains, to require from King Otto the issue of a liberal Constitution to the state, which has been governed since independence (1830) by various domestic and foreign business interests.
Søren Kierkegaard's philosophical book Fear and Trembling is first published.
William Rowan Hamilton discovers the calculus of quaternions and deduces that they are non-commutative.
November 17 – The city of Shanghai opens for trade with foreigners for the first time, welcoming a party of traders from the United Kingdom.
November 25 – Mount Etna erupts in Italy and kills 69 people in the village of Bronte.
December 9 – Bishop's University is founded as Bishop's College by Bishop George Jehoshaphat Mountain in Lennoxville, Quebec, for the education of members of the Church of England.
December 13 – Basutoland becomes a British protectorate.
December 17 – Charles Dickens' novella A Christmas Carol is first published, in London. Released on December 19 it sells out by Christmas Eve.
December 21 – The first total solar eclipse of Saros 139 occurs over southern Asia.
December – The world's first Christmas cards, commissioned by Sir Henry Cole in London from the artist John Callcott Horsley, are sent.
James Joule experimentally finds the mechanical equivalent of heat.
The steam powered rotary printing press is invented by Richard March Hoe in the United States.
Saint Louis University School of Law becomes the first law school west of the Mississippi River.
Germans from the Black Forest region of Southern Baden migrate to Venezuela.
Frederick Abberline, Chief Inspector of the London Metropolitan Police and investigator in the Jack the Ripper murders (d. 1929)
John H. Moffitt, American politician (d. 1926)
January 10 – Frank James, American outlaw (d. 1915)
January 25 – Hermann Schwarz, German mathematician (d. 1921)
January 29 – William McKinley, 25th President of the United States (d. 1901)
February 6 – Frederic W. H. Myers, British poet (d. 1901)
February 19 – Adelina Patti, Spanish opera singer (d. 1919)
February 22 – Rudolf Montecuccoli, Austro-Hungarian admiral (d. 1922)
March 7 – Tsuboi Kōzō, Japanese admiral (d. 1898)
March 15 – Arichi Shinanojō, Japanese admiral (d. 1919)
March 17 – Henry Ware Lawton, American general (d. 1899)
April 4 – William Henry Jackson, American explorer and photographer (d. 1942)
April 15 – Henry James, American novelist (d. 1916)
April 25 – Princess Alice of the United Kingdom, third child of Queen Victoria (d. 1878)
May 20 – Itō Sukeyuki, Japanese admiral (d. 1914)
May 21 – Charles Albert Gobat, Swiss politician, recipient of the Nobel Peace Prize (d. 1914)
June 1 – Henry Faulds, Scottish physician, missionary and fingerprinting pioneer (d. 1930)
June 3 – King Frederick VIII of Denmark (d. 1912)
June 9 – Bertha von Suttner, Austrian writer and pacifist, recipient of the Nobel Peace Prize (d. 1914)
June 15 – Edvard Grieg, Norwegian composer (d. 1907)
June 30 – Sir Ernest Satow, British diplomat and scholar (d. 1928)
July 7 – Camillo Golgi, Italian physician, recipient of the Nobel Prize in Physiology or Medicine (d. 1926)
July 17 – Penn Symons, British general (d. 1899)
July 19 – Francis J. Higginson, United States Navy admiral (d. 1931)
July 29 – Johannes Schmidt, German linguist (d. 1901)
August 1 – Robert Todd Lincoln, American politician and businessman (d. 1926)
August 10 – Joseph McKenna, American politician and Associate Justice of the Supreme Court of the United States (d. 1926)
August 20 – Christina Nilsson, Swedish operatic soprano (d. 1921)
August 31 – Georg von Hertling, Chancellor of Germany (d. 1919)
September 4 – Ján Levoslav Bella, Slovak composer (d. 1936)
September 23 – Melville Reuben Bissell, American entrepreneur and inventor of the Carpet sweeper (d. 1889)
September 29 – Mikhail Skobelev, Russian general (d. 1882)
October 4 – Marie-Alphonsine Danil Ghattas, Palestinian Catholic nun, canonized (d. 1927)
October 25 – Pierre Lallement, French inventor of the bicycle (d. 1891)
November 19 – C. X. Larrabee, American businessman (d. 1914)
November 25 – Henry Ware Eliot, American industrialist, philanthropist and father of T. S. Eliot (d. 1919)
November 27 – Cornelius Vanderbilt II, American railway magnate (d. 1899)
November 29 – Gertrude Jekyll, English garden designer, writer and artist (d. 1932)
November 30 – Martha Ripley, American physician (d. 1912)
December 3 – William Forbes Gatacre, British general (d. 1906)
December 11 – Heinrich Hermann Robert Koch, German physician, recipient of the Nobel Prize in Physiology or Medicine (d. 1910)
December 28 – Colonel Prentiss Ingraham, American author of dime fiction (d. 1904)
Joseph James Cheeseman, Liberian politician, 12th President of Liberia (d. 1896)
Annetta Seabury Dresser, American writer (d. 1935)
Edmund William Berridge, British medical doctor (d. 1923)
Jang Seung-eop, Korean painter (d. 1897)
Sophia Tavoularis, Greek actor (d. 1916)
Adelaida Lukanina, Russian chemist (d. 1908)
Antoine Bournonville, French ballet dancer and choreographer (b. 1760)
Francis Scott Key, American songwriter of The Star-Spangled Banner (b. 1779)
March 3 – David Porter, American naval officer (b. 1780)
Guadalupe Victoria, Mexican revolutionary (b. 1786)
Robert Southey, English poet (b. 1774)
March 25 – Robert Murray M'Cheyne, Scottish clergyman (b. 1813)
March 27 – Karl Salomo Zachariae von Lingenthal, German jurist (b. 1769)
April 17 – Samuel Morey, American inventor (b. 1762)
May 28 – Noah Webster, American lexicographer (b. 1758)
June 1 – William Abbot, English actor (b. 1798)
June 7 – Friedrich Hölderlin, German writer (b. 1770)
July 2 – Samuel Hahnemann, German physician (b. 1755)
July 7 – John Holmes, American politician (b. 1773)
July 14 – Miguel de Álava, Spanish soldier and statesman (b. 1770)
August – Sequoyah, Native American silversmith, creator of the Cherokee syllabary (b. c. 1767)
July 22 – Marie-Madeleine Lachenais, Haitian de facto politician (b. 1778)
Howqua, Chinese merchant, "richest man in the world" (b. 1769)
Léopoldine Hugo, daughter of French novelist Victor Hugo (b. 1824)
September 11 – Joseph Nicollet, French geographer (b. 1786)
September 16 – Ezekiel Hart, Canadian entrepreneur and politician (b. 1770 or 1767)
November 10 – John Trumbull, American painter (b. 1756)
November 28 – József Ficzkó, Burgenland Croatian writer (b. 1772)
December 12 – King William I of the Netherlands (b. 1772)
December 18 – Thomas Graham, 1st Baron Lynedoch, British Governor-General of India (b. 1748)
1843 (MDCCCXLIII) was a common year starting on Sunday (dominical letter A) of the Gregorian calendar and a common year starting on Friday (dominical letter C) of the Julian calendar, the 1843rd year of the Common Era (CE) and Anno Domini (AD) designations, the 843rd year of the 2nd millennium, the 43rd year of the 19th century, and the 4th year of the 1840s decade. As of the start of 1843, the Gregorian calendar was 12 days ahead of the Julian calendar, which remained in localized use until 1923.