1656

January–June

• January 17 - The Treaty of Königsberg is signed, establishing an alliance between Charles X Gustav of Sweden and Frederick William, Elector of Brandenburg.
• January 24 - The first Jewish doctor in the Thirteen Colonies of America, Jacob Lumbrozo, arrives in Maryland.
• April 1 - Lwów Oath: John II Casimir Vasa, King of Poland, crowns the Black Madonna of Częstochowa as Queen and Protector of Poland in the cathedral of Lwów, after the miraculous saving of the Jasna Góra Monastery during the Deluge, an event which changed the course of the Second Northern War.
• April 2 - The Treaty of Brussels is signed, creating an alliance between Philip IV of Spain and the exiled Royalists of the British Isles, led by Charles II.
• April 28 - The ship Vergulde Draeck is wrecked off Ledge Point, Western Australia after it departs the Cape of Good Hope; rescue missions fail to find survivors.
• May 12 - The Dutch capture the city of Colombo, Sri Lanka, marking the start of Dutch Ceylon.

  July–December

• July - In an attempt to rescue survivors of the Vergulde Draeck, a search party is sent ashore, in Goede Hoop's boat, which smashes against rocks and sinks; 8 sailors drown; 3 more disappear ashore.
• July 27 - A Writ of Excommunication is issued against Baruch Spinoza.
• July 28–30 - Battle of Warsaw: Led by King Charles X Gustav of Sweden, the armies of the Swedish Empire and the Margraviate of Brandenburg defeat the forces of the Polish–Lithuanian Commonwealth, near Warsaw.
• September 15 - Köprülü Mehmed Pasha becomes Grand Vizier of the Ottoman Empire.
• December - The pendulum clock is invented by Christiaan Huygens.
• December 20 - The Treaty of Labiau is signed, between Charles X Gustav of Sweden and Frederick William, Elector of Brandenburg.

  Undated

• The Stockholm Banco, the first bank to issue banknotes, is founded in Stockholm, Sweden.
• The only English fifty shilling coin is minted.
• Konoike Zen'amon founds a baking and money-changing business in Osaka, Japan.
• Adams' Grammar School at Newport, Shropshire, England is founded by William Adams.
• Physician Samuel Stockhausen of the metal mining town of Goslar, Lower Saxony publishes his Libellus de lithargyrii fumo noxio morbifico, ejusque metallico frequentiori morbo vulgò dicto die Hütten Katze oder Hütten Rauch, a pioneering study of occupational disease.

  Births

• January 1 - William Fleetwood, Anglican bishop
• January 2 - Paolo Panelli, Italian painter
• January 14 - Duchess Johanna Magdalena of Saxe-Altenburg
• January 15 - John Ashburnham, 1st Baron Ashburnham, English politician
• January 29 - Samuel Andrew, American Congregational clergyman, educator
• February 2 - Charles Churchill
• February 9 - Rose Venerini, Italian saint, educational pioneer
• February 10 - Ferdinand de Marsin, Marshal of France
• February 16 - Anthony Cary, 5th Viscount of Falkland, English politician
• March 1 - Maria Angela Caterina d'Este, Italian princess
• March 2 - Jan Frans van Douven, Dutch painter
• March 11 - Duchess Marie Elisabeth of Hesse-Darmstadt
• March 13 - Hachisuka Tsunamichi, Japanese daimyō who ruled the Tokushima Domain
• March 26 - Nicolaas Hartsoeker, Dutch mathematician and physicist
• March 30 - Nicolas de Largillière, French painter
• March 31 - Giovanni Batista Bussi, Italian Catholic cardinal
• March 31 - Juan Andrés de Ustariz, Royal Governor of Cuba
• April 17 - William Molyneux, Irish politician, philosopher and writer
• April 9 - Francesco Trevisani, Italian painter
• April 10 - René Lepage de Sainte-Claire, lord-founder of Rimouski in eastern Quebec, Canada
• April 12 - Benoît de Maillet, French diplomat and natural historian
• April 23 - Anton Egon, Prince of Fürstenberg-Heiligenberg, Governor of the Electorate of Saxony
• May 2 - Sir Richard Levinge, 1st Baronet, British politician
• May 4 - John Louis I, Prince of Anhalt-Dornburg
• May 8 - Sir John Mainwaring, 2nd Baronet, English Member of Parliament
• May 23 - Rebecca Rawson, Massachusetts heroine of the 1849 book Leaves from Margaret Smith's Journal
• May 28 - Anton Florian, Prince of Liechtenstein
• May 31 - Marin Marais, French composer and viol player
• June 5 - Joseph Pitton de Tournefort, French botanist
• June 17 - Paul Thymich, German poet
• July 1 - Polykarp Leyser III, German Lutheran theologian
• July 4 - John Leake, English Royal Navy admiral
• July 5 - John Hamilton, 2nd Lord Belhaven and Stenton, Scottish politician
• July 7 - Guru Har Krishan, 8th Guru of Sikhism
• July 15 - Massimiliano Soldani Benzi, Italian artist
• July 15 - Gerard Langbaine, English dramatic biographer and critic
• July 16 - George Ashby, British politician
• July 18 - Joachim Bouvet, French Jesuit active in China
• July 20 - Johann Bernhard Fischer von Erlach, Austrian architect
• August 6 - Claude de Forbin, French naval commander
• August 12 - Claude de Visdelou, French missionary
• August 16 - Christian Knaut, German physician
• August 18 - Ferdinando Galli-Bibiena, Italian painter
• September 6 - Guillaume Dubois, French cardinal and statesman
• September 7 - Robert Molesworth, 1st Viscount Molesworth, Irish politician
• September 9 - Johann Caspar Ferdinand Fischer, German organist and composer
• September 9 - Thomas Hewet, English landowner and architect
• September 11 - Ulrika Eleonora of Denmark, Swedish queen
• September 14 - Thomas Baker, English antiquarian
• September 26 - William des Bouverie, British aristocrat and merchant
• October 2 - Hendrik Carré, Dutch painter
• October 20 - Nicolas de Largillière, French painter
• November 3 - Georg Reutter, German composer and organist
• November 8 - Edmond Halley, English scientist
• November 18 - Jacques de Tourreil, French lawyer
• November 20 - Eleonore Charlotte of Württemberg-Montbéliard, Duchess
• November 23 - Jacob de Heusch, Dutch painter
• December 2 - Joshua Oldfield, English Presbyterian divine
• December 11 - Johann Michael Rottmayr, Austrian painter
• date unknown
• * Patrick Abercromby, Scottish physician and antiquarian
• * Maria Oriana Galli-Bibiena, Italian painter
• * Kateri Tekakwitha, Native American beatified in the Roman Catholic Church

  Deaths

• January 3 - Mathieu Molé, French statesman
• January 18 - Augustus, Duke of Saxe-Lauenburg, German noble
• January 22 - Thomas Francis, Prince of Carignano
• February 13 - Ferdinando Hastings, 6th Earl of Huntingdon, English politician
• February 25 - Henriette Catherine de Joyeuse, Duke of Joyeuse
• March 21 - James Ussher, Archbishop of Armagh and Primate of All Ireland
• March 19 - Georg Calixtus, German Lutheran theologian who looked to reconcile all Christendom
• April 7 - Krzysztof Arciszewski, Polish-Lithuanian noble
• April 10 - Gerard Pietersz Hulft, Dutch general
• April 24 - Thomas Fincke, Danish mathematician and physicist
• April 27
• * Jan van Goyen, Dutch painter
• * Gerard van Honthorst, Dutch painter
• May 1 - Carlo Contarini, Doge of Venice
• May 17 - Dirck Hals, Dutch painter
• May 19 - George Louis, Prince of Nassau-Dillenburg, German noble
• June 5 - Francesco Cornaro, Doge of Venice
• June 9 - Thomas Tomkins, Welsh composer
• June 12 - Charles Worsley, English soldier and politician
• June 21 - Maximilian van der Sandt, Dutch theologian
• July 2 - François-Marie, comte de Broglie, Italian-born French commander
• July 12 - Giovanni Giacomo Barbelli, Italian painter
• August 8 - Brás Garcia de Mascarenhas, soldier, poet and writer
• August 11 - Ottavio Piccolomini, Austrian-Italian field marshal
• August 17 - Marie Anne d'Orléans, French princess
• August 24 - Aegidius Gelenius, German heraldist
• September 8 - Joseph Hall, English bishop and writer
• September 22 - Christian II, Prince of Anhalt-Bernburg
• October - Stephen Bachiler, English clergyman
• October 3 - Myles Standish, Mayflower colonist
• October 8 - John George I, Elector of Saxony
• October 12
• * Juan Alonso y Ocón, Spanish Catholic prelate, Archbishop of La Plata o Charcas
• * Juan Tellez-Girón y Enriquez de Ribera, 4th Duke of Osuna
• October 30 - Ferruccio Baffa Trasci, Italian bishop
• November 6
• * King John IV of Portugal
• * Jean-Baptiste Morin, French mathematician
• November 12
• * Albrycht Stanisław Radziwiłł, Polish nobleman
• * Hendrick van Anthonissen, Dutch painter
• December 2 - Alessandro dal Borro, Austrian Field Marshal
• December 20 - David Beck, Dutch portrait painter
• December 21 - Thomas Trevor, English politician and judge
• December 27 - Andrew White, Apostle of Maryland
• December 28 - Laurent de La Hyre, French Baroque painter
• date unknown - Meleki Hatun, influential Ottoman lady-in-waiting