January 16 – Treaty of Westminster signed between Great Britain and Prussia guaranteeing the neutrality of the German province of Hanover controlled by King George II of Great Britain.
January 27 – Wolfgang Amadeus Mozart is born.
March 17 – St. Patrick's Day is celebrated in New York City for the first time (at the Crown and Thistle Tavern).
April 12 – Seven Years' War: The French invade Minorca, at this time under British control.
May 18 – Seven Years' War: The Seven Years' War formally begins when Great Britain declares war on France.
May 20 – Seven Years' War – Battle of Minorca: The British fleet under John Byng is defeated by the French under Roland-Michel Barrin de La Galissonière.
20 June – A garrison of the British Army in India is imprisoned in the Black Hole of Calcutta.
June 25 – The Marine Society is founded in London, the world's oldest seafarers' charity.
June 29 – Seven Years' War – Siege of Fort St Philip at Port Mahon: The British garrison in Minorca surrenders to the French after two months' siege by Armand de Vignerot du Plessis.
June – The Coup of 1756, an attempted coup d'état planned by Queen Louisa Ulrika of Sweden to abolish the rule of the Riksdag of the Estates and reinstate absolute monarchy in Sweden with the support of the Hovpartiet, is exposed and subdued.
July 30 – Bartolomeo Rastrelli presents the newly built Catherine Palace to Empress Elizabeth and her courtiers.
August 14 – Seven Years' War – French and Indian War: Fort Oswego falls to the French.
August 29 – Frederick II of Prussia invades Saxony, beginning the Seven Years' War on the continent.
October 1 – Seven Years' War – Battle of Lobositz: Frederick defeats an Austrian army under Marshal Maximilian Ulysses Count Browne.
October 14 – An Agreement of Friendship and Trade is signed by the Sultan Osman III and the King Frederick V. Denmark has appointed an extraordinary representative to the Ottoman Empire.
December – Seven Years' War – French and Indian War: Militias of the Royal Colony of North Carolina build a fort on the province's western frontier to protect it against natives allied with the French. The fort is named Fort Dobbs in honor of North Carolina Governor Arthur Dobbs, who persuaded the North Carolina legislature to fund the construction a year earlier.
December 14 The play Douglas is performed for the first time in Edinburgh, with overwhelming success, in spite of the opposition of the local church presbytery, who summon Alexander Carlyle to answer for having attended its representation. However, it fails in its early promise to set up a new Scottish dramatic tradition.
Frederick II of Prussia forces his country's peasants to grow the unpopular and obscure potato.
The town of Gus-Khrustalny is established in Russia with the setting up of a crystal glass factory.
First chocolate-candy factory begins operations in Germany.
Leopold Mozart publishes his book on his method for learning to play the violin, Versuch einer gründlichen Violinschule.
January 19 – Guillaume-Antoine Olivier, French entomologist (d. 1814)
January 27 – Wolfgang Amadeus Mozart, Austrian composer (d. 1791)
February 6 – Aaron Burr, 3rd Vice President of the United States (d. 1836)
March 3 – William Godwin, English writer (d. 1836)
March 4 – Sir Henry Raeburn, Scottish painter (d. 1823)
May 18 – Ignaz Aurelius Fessler, court councillor and minister to Alexander I (d. 1839)
May 27 – King Maximilian I Joseph of Bavaria (d. 1825)
May 31 – Abbé Faria, Catholic monk (d. 1819)
June 6 – John Trumbull, American painter (d. 1843)
June 20 – Joseph Martin Kraus, German-Swedish composer (d. 1792)
July 7 – Gustaf Adolf Reuterholm, Swedish statesman (d. 1813)
July 31 – Dheeran Chinnamalai, Tamil king (d. 1805)
August 1 – Pierre Louis Prieur, French politician (d. 1827)
August 29 – Heinrich Graf von Bellegarde, Austrian field marshal and statesman (d. 1845)
September 7 – Willem Bilderdijk, Dutch author (d. 1831)
September 23 – John Loudon McAdam, Scottish engineer and road-builder (d. 1836)
October 21 – Philippine Engelhard, German writer and scholar (d. 1831)
October 28 – ALF, fictional alien
November 3 – Pierre Laromiguière, French philosopher (d. 1837)
January 18 – Francis George of Schönborn-Buchheim (b. 1682)
February 25 – Eliza Haywood, English actress and writer (b. 1693)
April 10 – Giacomo Antonio Perti, Italian composer (b. 1661)
April 18 – Jacques Cassini, French astronomer (b. 1677)
July 24 – George Vertue, English engraver and antiquary (b. 1684)
October 26 – Roland-Michel Barrin de La Galissonière, governor of New France (b. 1693)
October 28 – Charles Somerset, 4th Duke of Beaufort (b. 1709)
December 8 – William Stanhope, 1st Earl of Harrington, English statesman and diplomat (b. c. 1690)
date unknown – Bernard Accama, Dutch painter (b. 1697)
1756 (MDCCLVI) was a leap year starting on Thursday (dominical letter DC) of the Gregorian calendar and a leap year starting on Monday (dominical letter GF) of the Julian calendar, the 1756th year of the Common Era (CE) and Anno Domini (AD) designations, the 756th year of the 2nd millennium, the 56th year of the 18th century, and the 7th year of the 1750s decade. As of the start of 1756, the Gregorian calendar was 11 days ahead of the Julian calendar, which remained in localized use until 1923.