Year 1738 (MDCCXXXVIII) was a common year starting on Wednesday (link will display the full calendar) of the Gregorian calendar (or a common year starting on Sunday of the 11-day slower Julian calendar).

Events of 1738

January - June

• February 4 - Court Jew Joseph Suss Oppenheimer is executed in Württemberg.
• April 15 - Serse, an Italian opera by George Frideric Handel, premieres in London.
• May 24 - John Wesley is converted, essentially launching the Methodist movement; the day is celebrated annually by Methodists as Aldersgate Day.

July - December

• November 18 - The Treaty of Vienna is ratified.

Undated

• Russo-Turkish War (1735-1739): The Russian army fails to cross the Dniester. They are decimated by plague.
• China's Qing government announces that all western businessmen have to use the Cohong in Guangzhou to trade.
• The excavation of Herculaneum, a Roman city buried by Vesuvius in AD 79, begins.
• Stanis“aw Leszczy-ski receives Lorraine in exchange for renouncing the Polish throne.
• Pierre Louis Maupertuis publishes Sur la figure de la terre, which 'confirms Newton's view that the earth is a spheroid slightly flattened at the poles'.
• Franz Ketterer invents the cuckoo clock.
• Jacques de Vaucanson presents the world's first automaton, The Flute Player, to the French Academy of Sciences.

Births

• January 21 - Ethan Allen, American patriot (d. 1789)
• April 12 - Padre Francisco Garcés, Spanish missionary (d. 1781)
• April 14 - William Cavendish-Bentinck, 3rd Duke of Portland, Prime Minister of the United Kingdom (d. 1809)
• April 16 - Henry Clinton, British officer (d. 1795)
• May 1 - King Kamehameha I of Hawaii (d. 1819)
• May 27 - Nathaniel Gorham, American politician (d. 1796)
• June 4 - King George III of the United Kingdom (d. 1820)
• July 3 - John Singleton Copley, American painter (d. 1815)
• September 25 - Nicholas Van Dyke, American lawyer and President of Delaware (d. 1789)
• October 11 - Arthur Phillip, British admiral and Governor of New South Wales (d. 1814)
• October 18 - Andrei Bolotov, Russian agriculturalist and memoirist (d. 1833)
• November 15 - William Herschel, German-born astronomer (d. 1822)
• December 31 - Charles Cornwallis, 1st Marquess Cornwallis, British general (d. 1805)

Deaths

• February 15 - Matthias Braun, Czech sculptor (b. 1684)
• March 16 - George Bähr, German architect (b. 1666)
• March 25 - Turlough O'Carolan, Irish harper and composer (b. 1670)
• May 1 - Charles Howard, 3rd Earl of Carlisle, English statesman (b. c. 1669)
• May 15 - Sir John Chesshyre, English lawyer (b. 1662)
• June 5 - Isaac de Beausobre, French Protestant pastor (b. 1659)
• June 21 - Charles Townshend, 2nd Viscount Townshend, English politician (b. 1674)
• September 23 - Herman Boerhaave, Dutch humanist and physician (b. 1668)
• December 22 - Constantia Jones, English prostitute (executed) (b. c. 1708)