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1684 (MDCLXXXIV) was a leap year starting on Saturday of the Gregorian calendar and a leap year starting on Tuesday of the Julian calendar, the 1684th year of the Common Era (CE) and Anno Domini (AD) designations, the 684th year of the 2nd millennium, the 84th year of the 17th century, and the 5th year of the 1680s decade. As of the start of 1684, the Gregorian calendar was 10 days ahead of the Julian calendar, which remained in localized use until 1923.
- January – Edmond Halley, Christopher Wren and Robert Hooke have a conversation, in which Hooke later claimed not only to have derived the inverse-square law, but also all the laws of planetary motion.
- January 5 – King Charles II of England gives the title Duke of St Albans to Charles Beauclerk, his illegitimate son by Nell Gwyn.
- January 26 – Marcantonio Giustinian is elected Doge of Venice.
- March – The severe frost in Britain, which started the previous December, ends, during which the River Thames was frozen in London, and the sea as far as 2 miles (3.2 km) out from land froze over (there was great loss of beast and of wildlife, especially birds, and similar reports from across Northern Europe).
- April 5 - Karl Eusebius, Prince of Liechtenstein dies.
- April 25 – Morean War: The Republic of Venice declares war on the Ottoman Empire.
- July 24 – René-Robert Cavelier, Sieur de La Salle sails again from France, with a large expion designed to establish a French colony on the Gulf of Mexico, at the mouth of the Mississippi River.
- July 21–August 6 – Morean War: The Republic of Venice captures the Ottoman Fortress of Santa Maura.
- August 15
- September 21 – Morean War: The Republic of Venice captures the fortress town of Preveza from the Ottoman Empire.
- October 7 – Japanese Chief Minister Hotta Masatoshi is assassinated, leaving Shogun Tsunayoshi without any adequate advisors, leading him to issue impractical edicts and create hardships for the Japanese people.
- December 10 – Isaac Newton's derivation of Kepler's laws from his theory of gravity, contained in the paper De motu corporum in gyrum, is read to the Royal Society by Edmond Halley.
- December 20 – Miles Holmwood, known as Norway's Undead Soldier, is born (disappears in 1721, after the victory of the Great Northern War).
- December – The Tibet–Ladakh–Mughal war of 1679–84 ends.
- Pope Innocent XI forms a Holy League with the Habsburg Empire, Venice and Poland, to end the Ottoman Turkish rule in Europe.
- Japanese poet Saikaku composes 23,500 verses in 24 hours at the Sumiyoshi Shrine at Osaka; the scribes cannot keep pace with his dictation and just count the verses.
- Tokyo University, formally registered as a university in 1877, has its predecessor established.
- The British East India Company receives Chinese permission to build a trading station at Canton. Tea sells in Europe for less than a shilling a pound, but the import duty of 5 shillings makes it too expensive for most English people to afford; hence smuggled tea is drunk much more than legally imported tea.
- John Bunyan writes The Pilgrim's Progress, Part 2, in England.
- The Chipperfield's Circus dynasty begins, when James Chipperfield introduces performing animals to England, at the River Thames frost fairs in London.
- January 1 – Arnold Drakenborch, Dutch classical scholar (d. 1748)
- January 4
- January 14
- January 18 – Johann David Köhler, German historian (d. 1755)
- January 23 – Christian Rantzau, Danish noble (d. 1771)
- February 16 – Bohuslav Matěj Černohorský, Czech composer (d. 1742)
- February 19 – George Duckett (Calne MP), English politician (d. 1732)
- February 20 – Edward Bayly, Irish politician (d. 1741)
- February 21 – Justus van Effen, Dutch author (d. 1735)
- February 22 – Charles, Count of Armagnac, French noble (d. 1751)
- February 24 – Matthias Braun, Czech sculptor (d. 1738)
- March 2 – Christopher Wandesford, 2nd Viscount Castlecomer, 2nd Viscount Castlecomer and Member of Parliament (d. 1719)
- March 15 – Francesco Durante, Italian composer (d. 1755)
- March 19 – Jean Astruc, French physician and scholar (d. 1766)
- March 21 – Oley Douglas, English Member of Parliament (d. 1719)
- March 22
- March 24 – Samuel von Schmettau, Prussian field marshal (d. 1751)
- March 28 – Emperor Tekle Haymanot I of Ethiopia (d. 1708)
- March 31 – Francesco Durante, Neapolitan composer (d. 1755)
- April 2 – Henry Somerset, 2nd Duke of Beaufort (d. 1714)
- April 10 – Joseph Paris Duverney, French banker (d. 1770)
- April 15 – Catherine I of Russia (d. 1727)
- April 25 – Marco Benefial, Italian painter (d. 1764)
- May 2 – William Henry, Prince of Nassau-Usingen, Prince of Nassau-Usingen (1702-1718) (d. 1718)
- May 5 – Françoise Charlotte d'Aubigné, French noble (d. 1739)
- May 23 – Hachisuka Muneteru, Japanese daimyo of the Edo period (d. 1743)
- May 24 – Charles Alexander, Duke of Württemberg, regent of the Kingdom of Serbia (1720-1733) (d. 1737)
- May 27 – Wilhelm Reinhard von Neipperg, Austrian field marshal (d. 1774)
- May 31
- June 4 – Louis Charles, Duke of Schleswig-Holstein-Sonderburg-Franzhagen, German nobleman (d. 1707)
- June 6 – Nathaniel Lardner, English theologian (d. 1768)
- June 15 – Ernest Leopold, Landgrave of Hesse-Rotenburg, German noble (d. 1749)
- June 22 – Francesco Manfredini, Italian Baroque composer (d. 1762)
- July 3 – Jean-Baptiste Baudry, Canadian gunsmith (d. 1755)
- August 22 – Archduchess Maria Theresa of Austria (1684–1696) (d. 1696)
- August 24 – Sir Robert Munro, 6th Baronet, British politician (d. 1746)
- August 30 – Marguerite de Launay, baronne de Staal, French author (d. 1750)
- September 1 – Jaime Álvares Pereira de Melo, 3rd Duke of Cadaval (d. 1749)
- September 17
- September 18 – Johann Gottfried Walther, German music theorist, organist, and composer (d. 1748)
- September 22 – Charles Louis Auguste Fouquet, duc de Belle-Isle, French general and statesman (d. 1761)
- October 2 – Thomas Seaton, British poet (d. 1741)
- October 8 – Karl Aigen, Austrian painter (d. 1762)
- October 9 – Christopher of Baden-Durlach, German prince (d. 1723)
- October 10 – Jean-Antoine Watteau, French painter (d. 1721)
- October 16 – Peter Walkden, English writer (d. 1769)
- October 26 – Kurt Christoph Graf von Schwerin, Prussian Generalfeldmarschall (d. 1757)
- October 28 – Paul Alphéran de Bussan, French bishop (d. 1757)
- November 1 – Mikhail Mikhailovich Golitsyn (admiral), Russian naval officer (d. 1764)
- November 11 – Algernon Seymour, 7th Duke of Somerset (d. 1750)
- November 12 – Edward Vernon, English naval officer (d. 1757)
- November 15 – Paul-Hippolyte de Beauvilliers, duke of Saint-Aignan, French diplomat and soldier (d. 1776)
- November 16 – Allen Bathurst, 1st Earl Bathurst (d. 1775)
- December 3 – Ludvig Holberg, Norwegian historian and writer (d. 1754)
- December 9 – Abraham Vater, German antomist (d. 1751)
- December 14 – Siwart Haverkamp, Dutch classical scholar (d. 1742)
- December 15
- December 16 – Samuel Clark of St Albans, British theologian (d. 1750)
- December 21 – Ippolito Desideri, Italian tibetologist (d. 1733)
- December 31 – William Grimston, 1st Viscount Grimston, Irish noble (d. 1756)
- date unknown
- January 4 – Louis-Isaac Lemaistre de Sacy, French Bible translator (b. 1613)
- January 11 – Cornelis Speelman, Governor-General of the Dutch East Indies (b. 1628)
- January 13 – Henry Howard, 6th Duke of Norfolk (b. 1628)
- January 15 – Alvise Contarini, Doge of Venice (b. 1601)
- January 21 – Queen Myeongseong, Korean royal consort (b. 1642)
- January 29 – Angélique de Saint-Jean Arnauld d'Andilly, French Jansenist nun (b. 1624)
- February 5 – Dorothy Spencer, Countess of Sunderland, English countess (b. 1617)
- February 6 – Ernst Bogislaw von Croÿ, German Lutheran administrator (b. 1620)
- February 11 – Sir Thomas Peyton, 2nd Baronet, English politician (b. 1613)
- March 24 – Pieter de Hooch, Dutch painter (b. 1629)
- April 5
- April 3 – Marc Restout, French painter (b. 1616)
- April 6 – Domenico Maria Canuti, Italian painter of the Baroque period (b. 1625)
- April 13 – Nicolás Antonio, Spanish bibliographer born in Seville (b. 1617)
- April 24 – Johann Olearius, German hymnwriter (b. 1611)
- May 4 – John Nevison, English highwayman (b. 1639)
- May 10 – Anne Carr, Countess of Bedford, English noble (b. 1615)
- May 12 – Edme Mariotte, French physicist and priest (b. c. 1620)
- June 24 – Sir Edward Dering, 2nd Baronet, Irish politician (b. 1625)
- July 2 – John Rogers, American President of Harvard University (b. 1630)
- July 6 – Peter Gunning, English royalist churchman (b. 1614)
- July 26 – Elena Cornaro Piscopia, Venetian philosopher of noble descent (b. 1646)
- August 8 – George Booth, 1st Baron Delamer, England (b. 1622)
- August 20 – Maria d'Este, Italian noble (b. 1644)
- September 9 – Jakob Thomasius, German philosopher (b. 1622)
- October 1 – Pierre Corneille, French playwright (b. 1606)
- October 11 – James Tuchet, 3rd Earl of Castlehaven (b. c. 1617)
- October 12 – William Croone, English physician and one of the original Fellows of the Royal Society (b. 1633)
- October 15
- October 24 – Duchess Marie Elisabeth of Saxony (b. 1610)
- November 20 – Bartolomé Garcia de Escañuela, Spanish Catholic prelate and bishop (b. 1627)
- November 21 – Cornelius Van Steenwyk, American politician (b. 1626)
- November 23 – William Cavendish, 3rd Earl of Devonshire, English nobleman (b. 1617)
- December 10 – Sir Thomas Sclater, 1st Baronet, English politician (b. 1615)
- December 22 – Francis Hawley, 1st Baron Hawley, English politician (b. 1608)
- October – Dud Dudley, English ironmaster (b. 1600?)
- date unknown - Alexandra Mavrokordatou, Greek intellectual, salonist (b. 1605)