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1734 (MDCCXXXIV) was a common year starting on Friday of the Gregorian calendar and a common year starting on Tuesday of the Julian calendar, the 1734th year of the Common Era (CE) and Anno Domini (AD) designations, the 734th year of the 2nd millennium, the 34th year of the 18th century, and the 5th year of the 1730s decade. As of the start of 1734, the Gregorian calendar was 11 days ahead of the Julian calendar, which remained in localized use until 1923.
- January 8 – Salzburgers, Lutherans who were expelled by the Roman Catholic Bishop of Salzburg, Austria, in October 1731, set sail for the British Colony of Georgia, in America.
- March 12 – Salzburgers arrive at the mouth of the Savannah River, in the British Colony of Georgia.
- June 17 – French troops take Philippsburg, but the Duke of Berwick is killed.
- June 21 – In Montreal, New France, a black slave known by the French name of Marie-Joseph Angélique is tortured then hanged by the French authorities for allegedly setting a fire that destroyed part of the city.
- June 30 – War of the Polish Succession: Russian troops take Gdańsk (German: Danzig), which had been besieged since February 1734, after the failure of a French expedition to relieve the city.
- January 20 – Robert Morris, Founding Father of the United States (d. 1806)
- February 27 – Thomas Conway, American Revolutionary War general (d. 1800)
- March 1 – Jeanne de Bellem, heroine of the Brabant Revolution
- March 19 – Thomas McKean, American lawyer, signer of the Declaration of Independence (d. 1817)
- April 17 – King of Thonburi, King of Thailand (d. 1782)
- April – Elsa Beata Bunge, Swedish botanist (d. 1819)
- May 23 – Franz Mesmer, Austrian physician (d. 1815)
- July 25 – Ueda Akinari, Japanese author and scholar (d. 1809)
- September 3 – Joseph Wright, British painter (d. 1797)
- October 7 – Sir Ralph Abercromby, British general (d. 1801)
- November 2 – Daniel Boone, American frontiersman (d. 1820)
- December 15 – George Romney, English painter (d. 1802)
- December 17 – Maria I of Portugal, Portuguese queen from the Braganza Dynasty (d.1816)
- Date unknown – Catharina Ahlgren, Swedish poet, editor and early feminist (d.1800)
- Date unknown – Ulrica Arfvidsson, Swedish fortune teller (d. 1801)
- January 6 – John Dennis, English dramatist, critic (b. 1658)
- February 1
- February 9 – Diego de Astorga y Céspedes, Spanish Catholic cardinal (b. 1663)
- March 1 – Roger North, English biographer (b. 1653)
- March 16 – Andreas Silbermann, German organ builder (b. 1678)
- March 21 – Robert Wodrow, Scottish historian (b. 1679)
- April 1 – Louis Lully, French composer (b. 1664)
- April 25 – Johann Conrad Dippel, German alchemist (b. 1673)
- May 4 – James Thornhill, English painter (b. 1675 or 1676)
- May 15 – Sebastiano Ricci, Italian painter (b. 1659)
- May 24 – Georg Ernst Stahl, German physician and chemist (b. 1660)
- June 12 – James FitzJames, 1st Duke of Berwick, illegitimate son of James II of England and French military commander (b. 1670)
- June 15 – Giovanni Ceva, Italian mathematician (b. 1647)
- June 17 – Claude Louis Hector de Villars, Marshal of France (b. 1653)
- June 21 – Marie-Joseph Angélique, African slave
- July 22 – Peter King, 1st Baron King, Lord Chancellor of England (b. c. 1669)
- September 8 – Michel Sarrazin, Canadian scientist (b. 1659)
- November 14 – Louise de Kérouaille, Duchess of Portsmouth, French-born mistress of Charles II of England (b. 1649)
- December 28 – Rob Roy MacGregor, Scottish clan chief (b. 1671)