1680 (MDCLXXX) was a leap year starting on Monday of the Gregorian calendar and a leap year starting on Thursday of the Julian calendar, the 1680th year of the Common Era (CE) and Anno Domini (AD) designations, the 680th year of the 2nd millennium, the 80th year of the 17th century, and the 1st year of the 1680s decade. As of the start of 1680, the Gregorian calendar was 10 days ahead of the Julian calendar, which remained in localized use until 1923.
- January 2 – King Amangkurat II of Mataram personally stabs Trunajaya, who had led a failed rebellion against Mataram, during a ceremonial visit.
- February – Rev. Ralph Davenant's will provides for foundation of the Davenant Foundation School for poor boys in Whitechapel, in the East End of London.
- May – The volcano Krakatoa erupts, probably on a relatively small scale.
- June – Elizabeth Cellier, an English Catholic midwife, is tried and acquitted of treason for pamphleting against the government.
- July 8 – The first documented tornado in America kills a servant at Cambridge, Massachusetts.
- August 20 (August 10 Old Style) – The settlement of Karlskrona in Sweden is founded, as the Royal Swedish Navy relocates there.
- August 21 – Pueblo Revolt: Pueblo Indians capture Santa Fe (New Mexico) from the Spanish.
- August 24 – Comédie-Française is founded by decree of Louis XIV of France as La maison de Molière in Paris.
- October 9 – A massive earthquake that registered a magnitude of 9 Mw destroyed part of Málaga and other cities in the province of the same name.
- November 14 – The Great Comet of 1680 is first sighted.
- November 17 – Whigs organize processions to burn effigies of the Pope in London.
- Chambers of Reunion (French courts under Louis XIV) decide on the complete annexation of Alsace.
- The first Portuguese governor is appointed to Macau.
- The Riksdag of the Estates in Sweden enacts the Great Reduction, under which fiefs granted to the Swedish nobility are returned to the Crown, and the country becomes an absolute monarchy under King Charles XI.
- Johann Pachelbel writes his Canon in D Major
- January 23 – Joseph Ames, English author (d. 1759)
- February 14 – John Sidney, 6th Earl of Leicester, English privy councillor (d. 1737)
- February 23 – Jean-Baptiste Le Moyne de Bienville, French colonizer and Governor of Louisiana (d. 1767)
- April 9 – Philippe Néricault Destouches, French dramatist (d. 1754)
- April 23 – Anna Canalis di Cumiana, morganatic spouse of Victor Amadeus II of Savoy (d. 1769)
- June 22 – Ebenezer Erskine, Scottish religious dissenter (d. 1754)
- September 22 – Barthold Heinrich Brockes, German poet (d. 1747)
- October 19 – John Abernethy, Irish Protestant minister (d. 1740)
- date unknown – Bulleh Shah, Sufi poet (d. 1757)
- date unknown – Julianna Géczy, Hungarian heroine (d. 1714)
- approximate – Edward Teach (Blackbeard), English pirate (d. 1718)
- January 2
- January 18 – John Hervey, English courtier and politician (b. 1616)
- January 20 – Ann, Lady Fanshawe, English memoirist (b. 1625)
- January 23 – Capel Luckyn, English Member of Parliament (b. 1622)
- February – Ralph Davenant, English rector and founder of Davenant Foundation School
- February 11 – Elisabeth of the Palatinate, German princess, philosopher and Calvinist (b. 1618)
- February 17
- February 22 – Catherine Monvoisin, French fortune teller and poisoner (b. c. 1640)
- February 27 – Philippe Balthazar de Gand, French noble (b. 1616)
- March 14 – René Le Bossu, French critic (b. 1631)
- March 17
- March 23 – Nicolas Fouquet, French statesman (b. 1615)
- April 1 – David Denicke, German jurist and hymnwriter (b. 1603)
- April 3 – Chhatrapati Shivaji Bhosale, founder of the Maratha Empire (b. 1630)
- April 19 – Marie Hedwig of Hesse-Darmstadt, Duchess consort of Saxe-Meiningen (1671–1680) (b. 1647)
- April 25
- April 29 – Nicolas Cotoner, Spanish 61st Grandmaster of the Knights Hospitaller (b. 1608)
- May 29 – Abraham Megerle, Austrian composer and organist (b. 1607)
- May 31 – Joachim Neander, German Calvinist clergyman (b. 1650)
- June 4
- June 18 – Samuel Butler, English poet (b. 1612)
- June 10
- July 26
- July 30 – Thomas Butler, 6th Earl of Ossory (b. 1634)
- August 19 – John Eudes, French missionary (b. 1601)
- August 20 – William Bedloe, English informer (b. 1650)
- August 22 – John George II, Elector of Saxony (b. 1613)
- August 24
- August 25 – Symeon of Polotsk, Belarusian churchman and poet (b. 1629)
- August 27 – Joan Cererols, Catalan musician and Benedictine monk (b. 1618)
- August 28 – Charles I Louis, Elector Palatine (b. 1617)
- September 1 – Anna Sophia I, Abbess of Quedlinburg, Dutch abbess (b. 1619)
- September 2 – Per Brahe the Younger, Swedish soldier and statesman (b. 1602)
- September 3
- September 9 – Henry Marten, English regicide (b. 1602)
- September 10 – Baldassare Ferri, Italian castrato (b. 1610)
- September 11
- September 26 – John Dury, Scottish-born Calvinist minister (b. 1596)
- September 30 – Johann Grueber, Austrian Jesuit missionary and astronomer (b. 1623)
- October 4 – Pierre-Paul Riquet, French engineer and canal builder (b. 1609)
- October 13 – Lelio Colista, Italian composer and lutenist (b. 1629)
- October 16 – Raimondo Montecuccoli, Italian general (b. 1609)
- October 17 – Charles FitzCharles, 1st Earl of Plymouth, illegitimate son of King Charles II (b. 1657)
- October 30 – Antoinette Bourignon, Flemish mystic (b. 1616)
- November 9 – Hungerford Dunch, English politician (b. 1639)
- November 27 or November 28 – Athanasius Kircher, German Jesuit scholar (b. 1602)
- November 28
- November 30 – Peter Lely, Dutch painter (b. 1618)
- December 4 – Thomas Bartholin, Danish physician, mathematician, and theologian (b. 1616)
- December 8 – Henry Pierrepont, 1st Marquess of Dorchester, English politician (b. 1606)
- December 10 – Marco Uccellini, Italian composer and violinist (b. 1603 or 1610)
- December 20 – Princess Elisabeth Sophie of Saxe-Altenburg, German princess (b. 1619)
- December 29
- November 30 – Christopher Sandius, Dutch Arian writer (b. 1644)