Famous birthdays, deaths and events of 1634
- January 16 - Dorthe Engelbrechtsdatter, Norwegian poet (d. 1716)
- March 18 - Marie-Madeleine Pioche de la Vergne, comtesse de la Fayette
- June 20 - Charles Emmanuel II of Savoy, (d. 1675)
- October 23 - Hedvig Eleonora of Holstein-Gottorp, Queen of Sweden (d. 1715)
- May 12 - George Chapman, English writer
- June 25 - John Marston, English playwright (b. 1576)
- August 18 - Urbain Grandier, French priest (b. 1590)
- March 4 - Samuel Cole opens the first tavern in Boston, Massachusetts.
- March 25 - The first settlers arrive in Maryland.
- July 4 - The city of Trois-Rivières is founded in New France, later to become the Canadian province of Quebec.
- August 18 - Urbain Grandier, accused and convicted of sorcery, is burned alive in Loudun, France.
- October 11 - the Burchardi flood — "the second Grote Mandrenke" killed around 15,000 men in North Friesland, Denmark and Germany.
- November 11 - Following pressure from Anglican bishop John Atherton, the Irish House of Commons passes "An Act for the Punishment for the Vice of Buggery".