thumb|300px|right|[[April 20: Battle of Santa Cruz de Tenerife]]
Events
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January–March
- January 8 – Miles Sindercombe and his group of disaffected Levellers are betrayed in their attempt to assassinate Oliver Cromwell by blowing up the Palace of Whitehall in London and are arrested.
- January 29 – Rule of the Major-Generals (regional military government) in England is abolished.
- February 4 – Resettlement of the Jews in England: Oliver Cromwell gives Antonio Fernandez Carvajal the assurance of the right of Jews to remain in England.
- February 23 – In England, the Humble Petition and Advice offers Lord Protector Cromwell the crown.
- March 2 – The Great Fire of Meireki in Edo, Japan, destroys most of the city and damages Edo Castle, killing an estimated 100,000 people.
- March 23 – Anglo-Spanish War (1654–60): By the Treaty of Paris, France and England form an alliance against Spain; England will receive Dunkirk.
April–June
- April 20
- Anglo-Spanish War – Battle of Santa Cruz de Tenerife: English Admiral Robert Blake attempts to seize a Spanish treasure fleet.
- The Jews of New Amsterdam (later New York City) are granted freedom of religion, as full citizens.
- May 8 – Lord Protector Cromwell confirms his refusal of the crown of England, preferring the title "Lord Protector". and introduction of tea in England while coffee is introduced to France.
- Christiaan Huygens writes the first book to be published on probability theory, De ratiociniis in ludo aleae ("On Reasoning in Games of Chance").
- Andreas Gryphius' drama Katharina von Georgien is published in Breslau.
- Thomas Middleton's tragedy Women Beware Women (c. 1623–24) is published posthumously in London.
- February 10 – George Carpenter, 1st Baron Carpenter, English Army general (d. 1731)
- February 11 – Bernard Le Bovier de Fontenelle, French scientist and man of letters (d. 1757)
- February 21 – Blaise Gisbert, French Jesuit rhetorician and critic (d. 1731)
- February 24 – Clopton Havers, English physician (d. 1702)
- February 25 – Agathe de Saint-Père, French-Canadian business entrepreneur and inventor (d. 1748)
- March 1 – Samuel Werenfels, Swiss theologian (d. 1740)
- March 6 – Auguste Magdalene of Hessen-Darmstadt, German noblewoman and poet (d. 1674)
- March 18 – Giuseppe Ottavio Pitoni, Italian composer (d. 1743)
- March 19 – Jean Leclerc, Swiss theologian and biblical scholar (d. 1736)
- March 20 – Luigi Omodei (1607–1685), Italian Catholic cardinal (d. 1706)
- March 24 – Arai Hakuseki, Japanese politician and writer (d. 1725)
- April 16
- Thomas Fairfax, 5th Lord Fairfax of Cameron, English politician (d. 1710)
- Otto Friedrich von der Groeben, Prussian traveller, soldier and author (d. 1728)
- May 8 – Martino Altomonte, Italian painter (d. 1745)
- May 14 – Sambhaji, Maratha ruler (d. 1689)
- May 25 – Henri-Pons de Thiard de Bissy, French Catholic priest, bishop and cardinal (d. 1737)
- June 10 – James Craggs the Elder, English politician (d. 1721)
- June 14 – Sir William Blackett, 1st Baronet, of Newcastle-upon-Tyne, English politician (d. 1705)
- June 17 – Louis Ellies Dupin, French ecclesiastical historian (d. 1719)
- July 8 – Abraham de Peyster, New Amsterdam/New York politician (d. 1728)
- July 11 – King Frederick I of Prussia (d. 1713)
- July 12 – Friedrich Wilhelm III, Duke of Saxe-Altenburg (d. 1672)
- July 14 – William Cheyne, 2nd Viscount Newhaven, English politician (d. 1728)
- July 18 – Simon Digby, 4th Baron Digby, English politician (d. 1686)
- July 24
- Theodorus Janssonius van Almeloveen, Dutch classical scholar (d. 1712)
- Jean Mathieu de Chazelles, French hydrographer (d. 1710)
- July 25 – Philipp Heinrich Erlebach, German composer (d. 1714)
- August 7 – Henri Basnage de Beauval, French historian and lexicographer (d. 1710)
- August 9 – Pierre-Étienne Monnot, French sculptor (d. 1733)
- August 18
- Ferdinando Galli-Bibiena, Italian architect and painter (d. 1743)
- Antonio Margil, Spanish Franciscan missionary in North and Central America (d. 1726)
- September 14 – Sir Charles Blois, 1st Baronet, English politician (d. 1738)
- September 17
- Dudley Cullum, English politician and baronet (d. 1720)
- Pieter Schuyler, acting governor of the province of New York and army colonel (d. 1724)
- September 21 – Sultan Muhammad Akbar, Mughal prince (d. 1706)
- September 27 – Sofia Alekseyevna of Russia, Russian regent (d. 1704)
- September 29 – Heinrich of Saxe-Weissenfels, Count of Barby, German prince (d. 1728)
- October 2 – Guillaume Baudry, gunsmith and gold and silversmith in Lower Canada (d. 1732)
- October 4 – Francesco Solimena, Italian painter (d. 1747)
- October 8 – Wigerus Vitringa, Dutch painter (d. 1725)
- October 26 – Philipp, Duke of Saxe-Merseburg-Lauchstädt, German nobleman (d. 1690)
- November 6 – Joseph Denis, Canadian Rėcollet priest (d. 1736)
- November 12 – Anna Dorothea, Abbess of Quedlinburg (d. 1704)
- November 16 – Juliane Louise of East Frisia, Princess of East Frisia (d. 1715)
- November 26
- William Derham, English clergyman and natural philosopher (d. 1735)
- Michael Bernhard Valentini, German naturalist (d. 1729)
- November 28 – Philip Prospero, Prince of Asturias, heir apparent to the Spanish throne (d. 1661)
- December 2 – Franz Anton, Count of Hohenzollern-Haigerloch (d. 1702)
- December 8 – Changning, prince of the Qing dynasty (d. 1703)
- December 14 – Edmund Dunch, English Whig politician (d. 1719)
- December 15
- Michel Richard Delalande, French composer (d. 1726)
- Louis Thomas, Count of Soissons, Count of Soissons and Prince of Savoy (d. 1702)
- December 23
- Hannah Duston, Massachusetts Puritan mother of 8, taken captive during King William's War (d. 1736)
- Josiah Franklin, English-born American businessman, father of Benjamin Franklin (d. 1745)
- December 28 – Domenico Rossi, Swiss-Italian architect (d. 1737)
Deaths
thumb|right|110px|[[Robert Blake (admiral)|Robert Blake]]
thumb|right|110px|[[Jacob van Campen]]
- January 24 – Claude, Duke of Chevreuse (b. 1578)
- February 2 – Nicole, Duchess of Lorraine, French noble (b. 1608)
- February 7 – Cesare Dandini, Italian painter (b. 1596)
- February 8 – Laura Mancini, French court beauty (b. 1636)
- February 10 – Sebastian Stoskopff, French painter (b. 1597)
- February 19 – Jean Riolan the Younger, French anatomist (b. 1577)
- March – Edward Hopkins, colonial Connecticut politician (b. 1600)
- March 7 – Hayashi Razan, Japanese neo-Confucianist scholar (b. 1583)
- March 10 – Barthold Nihus, Roman Catholic priest (b. 1590)
- April ? – Richard Lovelace, English Cavalier poet (b. 1617)
- April 2
- Ferdinand III, Holy Roman Emperor (b. 1608)
- Jean-Jacques Olier, French Catholic priest (b. 1608)
- April 29 – Sophie Elisabeth Pentz, daughter of Christian IV of Denmark (b. 1619)
- May 7 – Nabeshima Katsushige, Japanese daimyō (b. 1580)
- May 9 – William Bradford, Governor of Plymouth Colony (b. 1590)
- May 10 – Gustav Horn, Count of Pori, Swedish soldier and politician (b. 1592)
- May 16 – Andrzej Bobola, Polish Jesuit missionary (b. 1591)
- June 3 – William Harvey, English physician (b. 1578)
- June 26 – Tobias Michael, German composer and cantor (b. 1592)
- July 17 – Eleonore Marie of Anhalt-Bernburg, Duchess consort of Mecklenburg-Güstrow (b. 1600)
- August 6 – Bohdan Khmelnytsky, Ukrainian Cossack Hetman (b. c. 1595)
- August 14 – Giovanni Paolo Lascaris, Italian 57th Grandmaster of the Knights Hospitaller (b. 1560)
- August 19 – Frans Snyders, Flemish painter (b. 1579)
- August 7 – Robert Blake, British admiral (b. 1599)
- August 29 – John Lilburne, English dissenter (b. c. 1614)
- September 1 – Arnold Vinnius, Dutch lawyer (b. 1588)
- September 7 – Arvid Wittenberg, Swedish field marshal and statesman (b. 1606)
- September 13 – Jacob van Campen, Dutch artist (b. 1596)
- September 23 – Joachim Jungius, German mathematician and philosopher (b. 1587)
- September 27 – Olimpia Maidalchini, politically active Roman noble (b. 1591)
- October 4 – Prince Maurice of Savoy, Catholic cardinal and Prince of Savoy (b. 1593)
- October 23 – Domenico Massenzio, Italian baroque composer (b. 1586)
- November 5 – Charles II, Duke of Elbeuf, French noble (b. 1596)
- November 10 – Anders Bille, Danish general (b. 1600)
- November 18 – Luke Wadding, Irish Franciscan friar and historian (b. 1588)
- November 20 – Sir Hugh Cholmeley, 1st Baronet, English politician (b. 1600)
- December 5 – Johan Oxenstierna, Swedish count and statesman (b. 1611)
- December 24 – Philippe Le Sueur de Petiville, French poet (b. 1607)
- date unknown – Willem Bontekoe, Dutch sea captain (b. 1587)