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1736 (MDCCXXXVI) was a leap year starting on Sunday of the Gregorian calendar and a leap year starting on Thursday of the Julian calendar, the 1736th year of the Common Era (CE) and Anno Domini (AD) designations, the 736th year of the 2nd millennium, the 36th year of the 18th century, and the 7th year of the 1730s decade. As of the start of 1736, the Gregorian calendar was 11 days ahead of the Julian calendar, which remained in localized use until 1923.
- Neustrelitz becomes the capital of Mecklenburg-Strelitz.
- Bushehr is founded in Persia.
- The Belgrade Fortress is completed.
- George Hamilton, 1st Earl of Orkney, becomes the first Field Marshal of Great Britain.
- A fire in the Russian city of Saint Petersburg burns 2,000 houses.
- A fire in Stony Stratford, England consumes 53 houses.
- One of the earliest records of use of a bathing machine is made at Scarborough, England.
- Charles Marie de La Condamine, with François Fresneau Gataudière, makes the first scientific observations of rubber, in Ecuador.
- Leonhard Euler produces the first published proof of Fermat's "little theorem." 
- Sir Isaac Newton's Method of Fluxions (1671), describing his method of differential calculus, is first published (posthumously) and Thomas Bayes publishes a defense of its logical foundations (anonymously).
- Muhammad ibn Abd al-Wahhab writes the Kitab at-tawhidt, marking the beginning of Wahhabism.
- The Haidamakas raid the shtetl of Pavoloch, killing 35.
- January 7 – Andrew Adams, American judge (d. 1797)
- January 19 – James Watt, Scottish inventor (d. 1819)
- January 25 – Joseph-Louis Lagrange, Italian-born mathematician (d. 1813)
- February 3 – Johann Georg Albrechtsberger, Austrian musician (d. 1809)
- February 29 – Ann Lee, English-born American religious leader (d. 1784)
- May 8 – Caterina Dolfin, Italian (Venetian) poet (d. 1793)
- May 10 – George Steevens, English literary critic (d. 1800)
- May 29 – Patrick Henry, American patriot (d. 1799)
- June 3 – Sir John Acton, 6th Baronet, Prime Minister of Naples (d. 1811)
- June 7 – Fermín Lasuén, Spanish missionary (d. 1803)
- June 14 – Charles-Augustin de Coulomb, French physicist (d. 1806)
- June 21 – Enoch Poor, American general (d. 1780)
- June 25 – John Horne Tooke, English politician, philologist (d. 1812)
- July – Juan Bautista de Anza, Governor of the Spanish Province of New Mexico (d. 1788)
- July 6 – Daniel Morgan, American pioneer, Congressman from Virginia, and general (d. 1802)
- August 9 – Louis Joseph, Prince of Condé (d. 1818)
- August 15 – Alexander Runciman, Scottish painter (d. 1785)
- August 26 – Jean-Baptiste L. Romé de l'Isle, French geologist (d. 1790)
- September 15 – Jean Sylvain Bailly, French astronomer (d. 1793)
- September 16 – Carter Braxton, signer of the American Declaration of Independence (d. 1797)
- October 27 – James Macpherson, Scottish poet (d. 1796)
- date unknown
- January 8 – Jean Leclerc (theologian), Swiss theologian and biblical scholar (b. 1657)
- January 17 – Matthäus Daniel Pöppelmann, German architect (b. 1662)
- January 31 – Filippo Juvarra, Italian architect (b. 1678)
- February 1 – James Stanley, 10th Earl of Derby, English politician (b. 1664)
- February 7 – Stephen Gray, English dyer, astronomer, and scientist (b. 1666)
- March 16 – Giovanni Battista Pergolesi, Italian composer (b. 1710)
- March 25 – Nicholas Hawksmoor, British architect (b. c. 1661)
- April 24 – Prince Eugene of Savoy, French-born Austrian general (b. 1663)
- April 30 – Johann Albert Fabricius, German scholar and bibliographer (b. 1668)
- May 9 – Diogo de Mendonça Corte-Real, Portuguese politician (b. 1658)
- August 14 – Victor Honoré Janssens, Flemish painter (b. 1658)
- September 16 – Daniel Gabriel Fahrenheit, German physicist and inventor (b. 1686)
- October 22 – George Clarke, English politician, architect (b. 1661)
- November 2 – Louis Antoine de Pardaillan de Gondrin, French duke (b. 1664)
- December 10 – António Manoel de Vilhena, Portuguese 66th Grandmaster of the Knights Hospitaller (b. 1663)
- December 12 (burial) – Antonina Houbraken, Dutch draughtswoman (b. 1686)
- December 22 – Sir William Robinson, 1st Baronet, British politician (b. 1655)
- December 26 – Antonio Caldara, Italian composer (b. 1670)
- date unknown