|Covid-19|February 14 – Henry Pelham becomes Prime Minister of Great Britain.
February 21 – George Frideric Handel's oratorio, Samson premieres in London.
March 2 – Battle of La Guaira: a British expeditionary fleet under Sir Charles Knowles is defeated by the Spanish.
May 10 – In New France, Governor Jean-Baptiste Le Moyne de Bienville ends his final term (multiple times over 43 years) as Governor of colonial French Louisiana, which he helped colonize; he is succeeded by the Marquis de Vaudreuil (for the next 10 years) and returns to France.
May 30 – The Dalecarlian rebellion (1743) in Sweden.
June 27 (June 16 O.S.) – War of the Austrian Succession: Battle of Dettingen in Bavaria – British forces, in alliance with those of Hanover and Hesse, defeat a French army under the duc de Noailles; King George II of Great Britain (and Elector of Brunswick) leads his own troops, the last British king to do so.
August 7 – Russia and Sweden sign the Treaty of Åbo.
September 11 – Natalia Lopukhina is flogged in front of the Twelve Collegia building in Saint Petersburg.
September 13 – The Treaty of Worms is signed between Great Britain, Austria, and Sardinia.
November 5 – Coordinated scientific observations of the transit of Mercury are organized by Joseph-Nicolas Delisle.
The last wolf in Scotland is thought to have been shot in 1743, in the town of Killiecrankie.
January 1 – Sir William Parker, 1st Baronet, of Harburn, British admiral (d. 1802)
January 18 – Louis Claude de Saint-Martin, French philosopher, known as le philosophe inconnu (d. 1803)
January 25 – Friedrich Heinrich Jacobi, German philosopher (d. 1819)
February 13 – Sir Joseph Banks, British naturalist and botanist (d. 1820)
February 19 – Luigi Boccherini, Italian composer (d. 1805)
February 23 – Mayer Amschel Rothschild, German-born banker (d. 1812)
February 28 – René Just Haüy, French "Father of Modern Crystallography" (d. 1822)
c. March/April – Joseph Brant, Mohawk leader (d. 1807)
March 4 – Johann David Wyss, Swiss author (d. 1818)
March 14 – Hannah Cowley, English dramatist and poet (d. 1809)
April – Etta Palm d'Aelders, Dutch-French feminist (d. 1799)
April 1 – Richard Butler (general) American soldier (d. 1793)
April 13 – Thomas Jefferson, 3rd President of the United States, author of the Declaration of American Independence (d. 1826)
May 14 – Louis Lebègue Duportail French military leader in the Continental Army during the American Revolutionary War (d. 1802)
May 17 – Seth Warner American revolutionary hero (d. 1784)
May 20 – Toussaint Louverture, Haitian rebel (d. 1803)
May 24 – Jean-Paul Marat, French revolutioner, doctor, scientist (d. 1793)
June 2 – Alessandro Cagliostro, Italian Freemason (d. 1795)
June 3 – José Fernando de Abascal y Sousa, Spanish viceroy of Peru (d. 1821)
June 3 – Lucia Galeazzi Galvani, Italian scientist (d. 1788)
August 26 – Antoine Lavoisier, French chemist (d. 1794)
September 11 – Nikolaj Abraham Abildgaard, Danish painter (d. 1809)
September 17 – Marquis de Condorcet, French mathematician, philosopher, and political scientist (d. 1794)
November 11 – Carl Peter Thunberg, Swedish botanist (d. 1828)
December 1 – Martin Heinrich Klaproth, German chemist who discovered uranium (1789), zirconium (1789), and cerium (1803) (d. 1817)
December 23 – Ippolit Bogdanovich, Russian poet (d. 1803)
date unknown – Károly Hadaly, Hungarian mathematician (d. 1834)
Elisabeth Christina von Linné, Swedish botanist (d. 1782)
January 3 – Ferdinando Galli-Bibiena, Italian architect/painter (b. 1657)
January 29 – Cardinal André-Hercule de Fleury, Bishop of Fréjus, chief minister of France under Louis XV (b. 1653)
January 29 – Charles-Irénée Castel de Saint-Pierre, French writer (b. 1658)
February 18 – Anna Maria Luisa de' Medici, last of the Medicis (b. 1667)
April 4 – Daniel Neal, English historian (b. 1678)
May 6 - Andrew Michael Ramsay, English Freemason (b. 1686)
June 16 – Louise-Françoise de Bourbon, eldest daughter of Louis XIV and Madame de Montespan; she built the Paris Palais Bourbon where she died (b. 1673)
July 2 – Spencer Compton, 1st Earl of Wilmington, second Prime Minister of the United Kingdom
August 5 – John Hervey, 2nd Baron Hervey, English statesman and writer (b. 1696)
September 14 – Nicolas Lancret, French painter (b. 1690)
September 21 – Jai Singh II, King of Amber-Juiper, India (b. 1688)
September 23 – Erik Benzelius the younger, Swedish priest (b. 1675)
October 4 – John Campbell, 2nd Duke of Argyll, Scottish soldier (b. 1678)
December 27 – Hyacinthe Rigaud, French painter (b. 1659)
Manuela Desvalls Vergós, Spanish political writer and agent.
1743 (MDCCXLIII) was a common year starting on Tuesday (dominical letter F) of the Gregorian calendar and a common year starting on Saturday (dominical letter B) of the Julian calendar, the 1743rd year of the Common Era (CE) and Anno Domini (AD) designations, the 743rd year of the 2nd millennium, the 43rd year of the 18th century, and the 4th year of the 1740s decade. As of the start of 1743, the Gregorian calendar was 11 days ahead of the Julian calendar, which remained in localized use until 1923.