|Covid-19|February 24–25 – Rebel Scots and Irish soldiers kill Bohemian military leader Albrecht von Wallenstein at Cheb.
March 1 – Battle of Smolensk: King Władysław IV Vasa of Poland defeats the Russian army.
March 25 – Leonard Calvert arrives in Maryland with Jesuit missionaries Andrew White, John Altham Gravenor, and Thomas Gervase, establishing St. Mary's as the fourth permanent settlement in British North America. In this year they also establish an institution of higher learning here which later becomes Georgetown University, North America's oldest university.
June 14 – The Treaty of Polyanovka is signed between the Polish–Lithuanian Commonwealth and the Tsardom of Russia, concluding the Smolensk War.
July 4 – The city of Trois-Rivières is founded in New France (the modern-day Canadian province of Quebec).
August (prob.) – Jean Nicolet becomes the first European to set foot in Wisconsin. He is in search of a water-route to the Pacific when he lands at Green Bay (Lake Michigan).
August 18 – Urbain Grandier, a priest accused of sorcery, is burned alive in Loudun, France.
September 5–6 – The Battle of Nördlingen results in a decisive victory for the Army of the Holy Roman Empire and Habsburg Spain.
October 11–12 – The Burchardi flood (also known as the second Grote Mandrenke) strikes the North Sea coast of Germany and Denmark, causing 8,000–12,000 deaths.
November 11 – The Irish House of Commons passes an Act for the Punishment of the Vice of Buggery.
Curaçao is captured by the Dutch.
The English establish a settlement at Cochin (modern-day Kochi) on the Malabar Coast.
Suspecting that Patriarch Afonso Mendes played a part in the Portuguese assault on Mombasa, Emperor Fasilides expels him and several Jesuit missionaries from Ethiopia.
The Académie française is founded by Cardinal Richelieu.
The first performance of the Oberammergau Passion Play is held in Bavaria.
Moses Amyraut's Traité de la predestination is published.
The Paulaner Brewery is established in Munich by Minim friars.
January 1 – Fleetwood Sheppard, English poet (d. 1698)
Sophia Eleonore of Hesse-Darmstadt, Landgravine consort of Hesse-Homburg (d. 1663)
Adam Krieger, German composer (d. 1666)
Katarzyna Sobieska, Polish noble (d. 1694)
January 16 – Dorothe Engelbretsdotter, Norway's first professional female author (d. 1713)
January 25 – Gaspar Fagel, Dutch statesman (d. 1688)
January 30 – Johann Hugo von Orsbeck, Archbishop-Elector of Trier (d. 1711)
February 5 – Maria Antonia Scalera Stellini, Italian poet (d. 1704)
February 6 – George Christian, Prince of East Frisia, Prince of Ostfriesland (d. 1665)
February 7 – Robert Robartes, Viscount Bodmin, English diplomat and politician (d. 1682)
February 8 – Teodósio, Prince of Brazil, Brazilian prince (d. 1653)
March 4 – Kazimierz Łyszczyński, Polish philosopher (d. 1689)
March 11 – Nicholas Gassaway, Colonel, Maryland Provincial Forces (d. 1691)
March 12 – Cornelis Kick, Dutch painter (d. 1681)
March 18 – Marie-Madeleine de La Fayette, French novelist (d. 1693)
March 20 – Balthasar Bekker, Dutch minister and author of philosophical and theological works (d. 1698)
March 23 – Philip Smythe, 2nd Viscount Strangford, Members of the Parliament of England (d. 1708)
March 25 – George Bull, English theologian and Bishop of St David's (d. 1710)
March 26 – Domenico Freschi, Opera composer (d. 1710)
March 28 – Sir Richard Temple, 3rd Baronet, Member of the English Parliament (d. 1697)
April 3 – Stanisław Jan Jabłonowski, Polish noble (d. 1702)
John Adolphus, Duke of Schleswig-Holstein-Sonderburg-Plön, German duke (d. 1704)
Joseph Alleine, Pastor, author (d. 1668)
April 9 – Countess Albertine Agnes of Nassau, Regent of Friesland, Groningen and Drenthe (1664–1679) (d. 1696)
April 14 – Sir John Reresby, 2nd Baronet, 17th-century English politician and diarist (d. 1689)
April 25 – Robert Montagu, 3rd Earl of Manchester, English politician (d. 1683)
May 4 – Lady Katherine Ferrers, English aristocrat and heiress (d. 1660)
May 7 – Richard Legh, English politician (d. 1687)
May 8 – Alexander Stuart, 5th Earl of Moray, Scottish nobleman (d. 1701)
June 1 – Roeloff Swartwout, American city founder (d. 1715)
June 6 – Maria Elisabeth of Holstein-Gottorp, Landgravine of Hesse-Darmstadt (d. 1665)
June 14 – Nathaniel Bond, English politician (d. 1707)
June 20 – Charles Emmanuel II, Duke of Savoy (d. 1675)
June 27 – Andreas Cleyer, German physician, pharmacist, botanist, and trader of the Dutch East India Company (d. 1698)
July 3 – Countess Palatine Dorothea Catherine of Birkenfeld-Bischweiler, Countess of Nassau-Ottweiler (d. 1715)
July 8 – Thomas Butler, 6th Earl of Ossory (d. 1680)
July 12 – John George I, Duke of Saxe-Eisenach, German duke (d. 1686)
July 14 – Pasquier Quesnel, French Jansenist theologian (d. 1719)
July 18 – Johannes Camphuys, Governor-General of the Dutch East Indies (d. 1695)
July 23 – Sir John Hoskyns, 2nd Baronet, English politician (d. 1705)
August 12 – Adam Colonia, Dutch Golden Age painter (d. 1685)
August 16 – Johann Daniel Major, German professor of theoretical medicine (d. 1693)
August 24 – Mary Eastey, American witch (d. 1692)
August 31 – Paul Amman (d. 1691)
September 4 – Robert South, English churchman who was known for his combative preaching (d. 1716)
September 6 – Thomas Tryon, British hat maker (d. 1703)
September 7 – Sir Richard Bulkeley, 1st Baronet, Irish politician (d. 1685)
September 22 – Christiana of Schleswig-Holstein-Sonderburg-Glücksburg, Duchess consort of Saxe-Merseburg (1650–1691) (d. 1701)
October 10 – Jan van Neck, Dutch painter (d. 1714)
October 14 – Alfonso IV d'Este, Duke of Modena, Italian noble (d. 1662)
October 18 – Luca Giordano, Italian late Baroque painter and printmaker in etching (d. 1705)
November 6 – Giuseppe Ghezzi, Italian painter (d. 1721)
November 7 – Francis Winnington, Solicitor-General for England and Wales (d. 1700)
November 23 – Paulet St John, 3rd Earl of Bolingbroke, English politician (d. 1711)
November 25 – Richard Slater, English politician (d. 1699)
November 27 – Roger Toothaker, Victim of the Salem witch trials (d. 1692)
November 28 – Marie Luise von Degenfeld, morganatic second wife of Charles I Louis (d. 1677)
December 15 – Thomas Kingo, Danish bishop (d. 1703)
December 22 – Mariana of Austria (d. 1696)
December 31 – Hotta Masatoshi, rōjū to Shogun Tokugawa Ietsuna (d. 1684)
February 25 – Albrecht von Wallenstein, general (assassinated) (b. 1583)
May 12 – George Chapman, English author (b. c.1559)
May 15 – Hendrick Avercamp, Dutch painter (b. 1585)
June 22 – Johann von Aldringen, Austrian field marshal (b. 1588)
June 25 – John Marston, English dramatist (b. 1576)
August 9 – William Noy, English jurist (b. 1577)
August 11 – Frederick Ulrich, Duke of Brunswick-Lüneburg (b. 1591)
August 18 – Urbain Grandier, French priest (b. 1590)
September 3 – Edward Coke, English colonial entrepreneur and jurist (b. 1552)
December 25 – Lettice Knollys, English noblewoman (b. 1540)
December 29 – John Albert Vasa, Polish bishop (b. 1612)
Adriano Banchieri, Italian composer (b. 1568)
Johan Bara, painter and engraver (b. c. 1581)
Wigund-Jeronym Trubecki, prince of Trubeck
1634 (MDCXXXIV) was a common year starting on Sunday (dominical letter A) of the Gregorian calendar and a common year starting on Wednesday (dominical letter E) of the Julian calendar, the 1634th year of the Common Era (CE) and Anno Domini (AD) designations, the 634th year of the 2nd millennium, the 34th year of the 17th century, and the 5th year of the 1630s decade. As of the start of 1634, the Gregorian calendar was 10 days ahead of the Julian calendar, which remained in localized use until 1923.