1720 was a leap year starting on Monday of the Gregorian calendar and a leap year starting on Friday of the Julian calendar, the 1720th year of the Common Era (CE) and Anno Domini (AD) designations, the 720th year of the 2nd millennium, the 20th year of the 18th century, and the 1st year of the 1720s decade. As of the start of 1720, the Gregorian calendar was 11 days ahead of the Julian calendar, which remained in localized use until 1923.
- January 21 – Sweden and Prussia sign the Treaty of Stockholm (Great Northern War).
- February 17 – The Treaty of The Hague is signed between Spain, Britain, France, Austria and the Dutch Republic, ending the War of the Quadruple Alliance.
- February 24 – Battle of Nassau – Spanish forces assault the British settlement of Nassau during the War of the Quadruple Alliance.
- February 29 – Queen Ulrika Eleonora of Sweden resigns, to let her husband Frederick I take over as king of Sweden. She had desired a joint rule, in a similar manner to William III and Mary II in Britain, but as the Swedish Riksdag of the Estates refuses this, she abdicates in her husband's favour instead.
- March 24 – The Riksdag of the Estates elects Frederick I new King of Sweden.
- April – "South Sea Bubble" in England: A scheme, for the South Sea Company to take over most of the unconsolidated national debt of Britain, massively inflates share prices.
- July 12 – The Lords Justice in Great Britain attempt to curb some of the excesses of the stock markets during the South Sea Bubble. They dissolve a number of petitions for patents and charters, and abolish more than 80 joint-stock companies of dubious merit, but this has little effect on the creation of "Bubbles", ephemeral joint-stock companies created during the hysteria of the times.
- August 14 – The Spanish Villasur expedition, which set out on June 16 from New Mexico, with the intention of checking French influence on the Great Plains of North America, ends in failure, as it is ambushed by a Pawnee and Otoe force.
- September – "South Sea Bubble": The English stock market crashes, with dropping prices for stock in the South Sea Company.
- November 16 – Pirate Calico Jack Rackham is brought to trial at Spanish Town in Jamaica; he is hanged at Port Royal two days later.
- January 2 – José de Gálvez, Spanish politician (d. 1787)
- January 4 – Johann Friedrich Agricola, German composer (d. 1774)
- January 13 – Richard Hurd, English bishop and writer (d. 1808)
- January 27 – Samuel Foote, English dramatist and actor (d. 1777)
- January 30 – Charles De Geer, Swedish industrialist, entomologist (d. 1778)
- February 8 – Emperor Sakuramachi of Japan (d. 1750)
- February 15 – Philippe Macquer, French historian (d. 1770)
- March 9 – Philip Yorke, 2nd Earl of Hardwicke, English politician (d. 1790)
- March 13 – Charles Bonnet, Swiss naturalist and writer (d. 1793)
- March 22 – Nicolas-Henri Jardin, French architect (d. 1799)
- April 23 – Vilna Gaon, Lithuanian rabbi (d. 1797)
- May 8 – William Cavendish, 4th Duke of Devonshire, Prime Minister of the United Kingdom (d. 1764)
- May 15 – Maximilian Hell, Slovakian astronomer (d. 1792)
- July 18 – Gilbert White, English naturalist and cleric (d. 1793)
- August 8 – Carl Fredrik Pechlin, Swedish politician (d. 1796)
- August 12 – Konrad Ekhof, German actor (d. 1778)
- August 18 – Laurence Shirley, 4th Earl Ferrers, English murderer (d. 1760)
- August 23 – Sybilla Masters, American inventor
- August 30 – Samuel Whitbread, English brewer, politician (d. 1796)
- October 3 – Johann Peter Uz, German poet (d. 1796)
- October 4 – Giovanni Battista Piranesi, Italian artist (d. 1778)
- October 8 – Jonathan Mayhew, American minister, patriot (d. 1766)
- October 8 – Geneviève Thiroux d'Arconville, French novelist, translator and chemist (d. 1805)
- October 19 – John Woolman, American Quaker preacher, abolitionist (d. 1772)
- November 1 – Toussaint-Guillaume Picquet de la Motte, French admiral (d. 1791)
- November 8 – Madeleine de Puisieux, French writer and active feminist (d. 1798)
- November 16 – Carlo Antonio Campioni, French-born composer (d. 1788)
- December 14 – Justus Möser, German statesman (d. 1794)
- December 24 – Anna Maria Mozart (née Pertl; d. 1778), wife of Leopold Mozart and mother of Wolfgang Amadeus Mozart and Maria Anna Mozart
- December 26 – Gian Francesco Albani, Italian Catholic cardinal (d. 1803)
- December 31 – Charles Edward Stuart, pretender to the British throne (d. 1788)
- January – Francis Daniel Pastorius, founder of Germantown, Pennsylvania (b. 1651)
- January 4 – Harry Mordaunt, British politician (b. 1663)
- January 10 – Ramon Perellos, Spanish 64th Grandmaster of the Knights Hospitaller (b. 1637)
- January 12 – William Ashhurst, Lord Mayor of London (1693–1694) (b. 1647)
- January 19 – Eleonor Magdalene of Neuburg, Holy Roman Empress (b. 1655)
- January 20
- January 31 – Thomas Grey, 2nd Earl of Stamford, English privy councilor (b. c. 1645)
- February 4 – Robert Wroth, British politician (b. 1660)
- February 27 – Samuel Parris, English-born Puritan minister (b. 1653)
- March 6 – Pieter van Bloemen, Flemish painter (b. 1657)
- March 13 – William Sewel, Dutch historian (b. 1653)
- July 12 – King Sukjong of Joseon (b. 1661)
- August 3
- August 9 – Simon Ockley, English orientalist (b. 1678)
- August 17 – Anne Lefèvre, French scholar (b. 1654)
- August 21 – John Leake, English Royal Navy admiral (b. 1656)
- August 26 – Johann Christoph Volkamer, German botanist (b. 1644)
- September 3 – Henri de Massue, Marquis de Ruvigny, 1st Viscount Galway, French soldier and diplomat (b. 1648)
- September 9 – Philippe de Courcillon, French officer and author (b. 1638)
- September 20 – Pierre de La Broue, American bishop (b. 1644)
- October 10 – Antoine Coysevox, French sculptor (b. 1640)
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