|Ab urbe condita||2491|
|Balinese saka calendar||1659–1660|
|British Regnal year||11 Geo. 2 – 12 Geo. 2|
|Chinese calendar||丁巳年 (Fire Snake)|
4434 or 4374
— to —
戊午年 (Earth Horse)
4435 or 4375
|- Vikram Samvat||1794–1795|
|- Shaka Samvat||1659–1660|
|- Kali Yuga||4838–4839|
|Japanese calendar||Genbun 3|
|Julian calendar||Gregorian minus 11 days|
|Minguo calendar||174 before ROC|
|Thai solar calendar||2280–2281|
1864 or 1483 or 711
— to —
1865 or 1484 or 712
|Wikimedia Commons has media related to 1738.|
1738 (MDCCXXXVIII) was a common year starting on Wednesday of the Gregorian calendar and a common year starting on Sunday of the Julian calendar, the 1738th year of the Common Era (CE) and Anno Domini (AD) designations, the 738th year of the 2nd millennium, the 38th year of the 18th century, and the 9th year of the 1730s decade. As of the start of 1738, the Gregorian calendar was 11 days ahead of the Julian calendar, which remained in localized use until 1923.
- February 4 – Court Jew Joseph Süß Oppenheimer is executed in Württemberg.
- February 11 – Jacques de Vaucanson stages the first demonstration of an early automaton, The Flute Player at the Hotel de Longueville in Paris, and continues to display it until March 30. 
- February 20 – Swedish Levant Company founded.
- March/April – Battle of the Dindar River: Emperor Iyasu II of Ethiopia is defeated by the Funj.
- April 15 – Serse, an Italian opera by George Frideric Handel, premieres in London.
- May 24 – John Wesley experiences a spiritual rebirth at a Moravian Church meeting in Aldersgate, in the City of London, essentially launching the Methodist movement; the day is celebrated annually by Methodists as Aldersgate Day (his younger brother Charles had a similar experience three days earlier).
- May 25 – The military phase of Cresap's War between the British North American Provinces of Maryland and Pennsylvania is ended when King George II of Great Britain negotiates a cease-fire.
- August 10 – Russo-Turkish War (1735–1739): The Russian army begins its attempt to cross the Dniester River and fails after three weeks; they are later decimated by plague. 
- September 18 – Samuel Johnson composes his first solemn prayer (published 1785).
- October 22 – The excavation of Herculaneum, a Roman city buried by Vesuvius in AD 79, begins near the Italian city of Resina on orders from King Charles VII of Spain to his engineer, Rocque Joaquin de Alcubierre. 
- November 18 – The Treaty of Vienna is ratified, ending the War of the Polish Succession. Under the terms of the treaty, Stanisław Leszczyński receives Lorraine, in exchange for renouncing the Polish throne.
- Specific date unknown: Carl Philipp Emanuel Bach, having completed a law degree, is hired as a court musician by Crown Prince Frederick of Prussia, the future Frederick the Great (Bach will remain in Frederick's service until 1768).
- China's Qing government announces that all western businessmen have to use the Cohong in Guangzhou to trade.
- Pierre Louis Maupertuis publishes Sur la figure de la terre, which confirms Newton's view that the earth is an oblate spheroid, slightly flattened at the poles.
- Black Forest clockmaker Franz Ketterer produces one of the earliest cuckoo clocks.
- Holy Royal Arch is founded.
- Rémy Martin is granted exclusive permission by King Louis XV of France to plant new vineyards, for impressing him with the quality of his cognac.
- January 21 – Ethan Allen, American patriot (d. 1789)
- February 6 – Pierre-Joseph Desault, French anatomist and surgeon (d. 1795)
- 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)
- May 27 – Nathaniel Gorham, American politician (d. 1796)
- May 28 – Joseph-Ignace Guillotin, French physician (d. 1814)
- June 4 – King George III of the United Kingdom (d. 1820)
- July 3 – John Singleton Copley, American painter (d. 1815)
- July 20 – Darejan Dadiani, Georgian queen consort (d. 1807)
- July 22 – Anne d'Yves, writer, participant in the Brabant Revolution (d. 1814)
- August 28 – Etteilla, French occult cartomancer (d. 1791)
- 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)
- January 6 – Franz Xaver Murschhauser, German composer and theorist (b. 1663)
- January 24 – Samuel Andrew, American Congregational clergyman, educator (b. 1656)
- January 27 – Marie Wulf, Danish pietist leader (b. 1685)
- January 30 – Benoît de Maillet, French diplomat and natural historian (b. 1656)
- February 9 – Béatrice Hiéronyme de Lorraine, Abbess of Remiremont (b. 1662)
- February 15 – Matthias Braun, Czech sculptor (b. 1684)
- February 27 – Henry Grove, English nonconformist minister (b. 1684)
- March 16 – George Bähr, German architect (b. 1666)
- March 25 – Turlough O'Carolan, Irish harper and composer (b. 1670)
- April 9 – Sir Charles Blois, 1st Baronet, English politician (b. 1657)
- 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)
- July 8 – Jean-Pierre Nicéron, French encyclopedist (b. 1685)
- July 28 – Heinrich, Duke of Saxe-Merseburg (b. 1661)
- September 23 – Herman Boerhaave, Dutch humanist, physician (b. 1668)
- December 22 – Constantia Jones, English prostitute (executed) (b. c. 1708)
- Kara Reilly, Automata and Mimesis on the Stage of Theatre History (Springer, 2011) pp83-84
- C. H. von Manstein, Memoirs of Russia, Historical, Political and Military, from the Year 1727 to 1744 (Beckett & DeHondt, 1770) pp203-210
- Pedar Foss and John J. Dobbins, The World of Pompeii (Routledge, 2009) p29
- "Rémy Martin". www.remymartin.com. Retrieved March 24, 2016.