1671

January–June

• April - Battle of Saraighat: Ahom general Lachit Borphukan defeats the Mughal forces on the outskirts of present day Guwahati, of then sovereign Assam.
• April 2 - In Rome, Pope Clement X canonizes Rose of Lima, making her the first Catholic saint of the Americas.
• May 9 - Thomas Blood, disguised as a clergyman, attempts to steal the Crown Jewels of the United Kingdom from the Tower of London. He is immediately caught, because he is too drunk to run with the loot. He is later condemned to death, and then mysteriously pardoned and exiled by King Charles II.
• June 22 - The Ottoman Empire declares war on Poland.

  July–December

• December - The first Seventh Day Baptist church in America is founded at Newport, Rhode Island.
• December 30 - The Académie royale d'architecture is founded by Louis XIV of France in Paris, France.

  Undated

• The first Jewish families settle in Berlin, moving from Vienna at the invitation of Frederick William, Elector of Brandenburg.

  Births

• January 11 - François-Marie, 1st duc de Broglie, French military leader
• February 26 - Anthony Ashley-Cooper, 3rd Earl of Shaftesbury, English politician and philosopher
• March 7 - Rob Roy MacGregor, Scottish folk hero
• April 6 - Jean-Baptiste Rousseau, French poet
• April 21 - John Law, Scottish economist
• May 24 - Gian Gastone de' Medici, Grand Duke of Tuscany
• June 8 - Tomaso Albinoni, Italian composer
• June 11 - Colley Cibber, English poet
• June 21 - Christian Detlev Reventlow, Danish diplomat and military leader, brother-in-law of king Frederick IV of Denmark,
• July 9 - Margareta von Ascheberg, Swedish land owner, countess and acting regimental colonel
• July 14 - Jacques d'Allonville, French astronomer and mathematician
• October 1 - Guido Grandi, Italian mathematician
• October 11 - King Frederick IV of Denmark
• November 6 - Colley Cibber, English actor-manager

  Deaths

• January 6 - Dubhaltach Mac Fhirbhisigh
• January 24 - Philipp, Prince of Hohenzollern-Hechingen
• January 25 - Henry X, Count of Reuss-Lobenstein, Rector of the University of Leipzig
• February 18 - John Mennes, English Royal Navy admiral
• February 19 - Charles Chauncy, English-born president of Harvard College
• February 22 - Adam Olearius, German scholar
• February 19 - Tokugawa Yorinobu, Japanese nobleman
• March 1
• * Marzio Ginetti, Italian Catholic cardinal
• * Leopold Wilhelm, Margrave of Baden-Baden, Imperial Field Marshal
• March 7 - Antonio de la Cerda, 7th Duke of Medinaceli, Grandee of Spain
• March 15 - Axel Urup, Danish general
• March 31 - Anne Hyde, wife of the future James II of England
• April 20 - Daniel Hay du Chastelet de Chambon, French mathematician
• April 23 - Theodorick Bland of Westover, American politician
• April 30
• * Petar Zrinski, Croatian Ban and nobleman
• * Fran Krsto Frankopan, Croatian poet and nobleman
• May 5 - Edward Montagu, 2nd Earl of Manchester, English politician
• May 8 - Sébastien Bourdon, French painter and engraver
• May 12 - Pedro de Villagómez Vivanco, Roman Catholic prelate, Archbishop of Lima, then Bishop of Arequipa
• May 16 - Sir John Langham, 1st Baronet, English Member of Parliament
• May 19 - John Scudamore, 1st Viscount Scudamore, English politician and Viscount
• June 2
• * Edward Leigh, English writer
• * Sophia Eleonore of Saxony, German duchess
• June 9 - Sebastian von Rostock, German bishop
• June 25 - Giovanni Battista Riccioli, Italian astronomer
• July 4 - Jan Cossiers, Flemish painter
• July 14 - Méric Casaubon, English classical scholar
• July 30 - Louis Joseph, Duke of Guise
• August 3 - Antonio Barberini, Italian Catholic cardinal
• August 10 - Sir John Evelyn, 1st Baronet, of Godstone, English noble
• September 1 - Hugues de Lionne, French statesman
• September 11 - Roshanara Begum, Mughal princess
• September 19 - Gilbert Ironside the elder, English bishop
• October 5 - Joachim Ernest, Duke of Schleswig-Holstein-Sonderburg-Plön
• October 26 - Sir John Gell, 1st Baronet, English politician
• November 12 - Thomas Fairfax, 3rd Lord Fairfax of Cameron, English Civil War general
• December 13 - Antonio Grassi, Italian Roman Catholic priest and beatus
• December 18 - Samuel Gott, English politician
• December 28 - Johann Friedrich Gronovius, German classical scholar