|Covid-19|January 9 – Philip Astley stages the first modern circus, with acrobats on galloping horses, in London.
February 11 – Samuel Adams's circular letter is issued by the Massachusetts House of Representatives and sent to the other Thirteen Colonies. Refusal to revoke the letter will result in dissolution of the Massachusetts Assembly and (from October) incur the institution of martial law to prevent civil unrest.
February 29 – A group of the szlachta, Polish nobles, establishes the Bar Confederation to defend the internal and external independence of the Polish–Lithuanian Commonwealth against Russian influence and against King Stanisław II Augustus.
May 10 – John Wilkes is imprisoned for writing an article for The North Briton severely criticizing King George III of Great Britain. This action provokes protesters to riot; in the Southwark district of London, troops fire on the mob, killing seven, the Massacre of St George's Fields.
May 15 – After the Treaty of Versailles, the island of Corsica is ceded by Genoa to France.
June 20 – Russo-Turkish War (1768–74), Russia captured the fortress of Bar.
August 8 – James Cook departs from Plymouth on his first voyage of discovery.
August 26 – The ship, The Endeavour set sail
December 1 – The slave ship Fredensborg sinks off Tromøy in Norway.
December 10 – Royal Academy founded in London, with Joshua Reynolds as its first President.
December 15 – The king's refusal to sign state documents results in the December Crisis (1768) in Sweden.
December 21 – King Prithvi Narayan Shah unifies several small kingdoms to establish the modern-day Nepal. This kingdom will collapse in 2008.
December 28 – Taksin is crowned as ruler of the Thonburi Kingdom in Thailand (through conquest) and establishes Thonburi as a capital.
The Petit Trianon, originally designed for Madame de Pompadour, is completed in the park of the Palace of Versailles and inaugurated by Louis XV of France.
New Smyrna, Florida, the largest attempt at colonization by the British in the New World, is founded by Dr. Andrew Turnbull.
A Secretary of State for the colonies is appointed in Britain.
Louis XV of France appoints René de Maupeou as chancellor and orders him to crush the judicial opposition.
Members of the Royal Society of Arts wrote The Complete Farmer: Or, a General Dictionary of Husbandry published in weekly numbers.
Louis Antoine de Bougainville discovers the Bougainville Strait and Bougainville Island.
First of the weekly numbers of the Encyclopædia Britannica, edited by William Smellie, are published in Edinburgh; one hundred are planned.
The Steller's sea cow, discovered on Bering Island in 1741, is driven to extinction.
January 1 – Maria Edgeworth, Irish novelist (d. 1849)
January 7 – Joseph Bonaparte, King of Naples and Spain (d. 1844)
January 17 – Smith Thompson, American politician and Associate Justice of the Supreme Court of the United States (d. 1843)
January 28 – King Frederick VI of Denmark (d. 1839)
February 12 – Francis II, Holy Roman Emperor (d. 1835)
February 13 – Édouard Mortier, duc de Trévise, French marshal (d. 1835)
March – Tecumseh (d. 1813)
March 21 – Joseph Fourier, French mathematician and physicist (d. 1830)
March 22 – Melesina Trench, Irish born writer and socialite (d. 1827)
May 3 – Charles Tennant, Scottish chemist and industrialist (d. 1838)
Caroline of Brunswick, queen of George IV of the United Kingdom (d. 1821)
Henry Paget, 1st Marquess of Anglesey, English general (d. 1854)
May 20 – Dolley Madison, First Lady of the United States (d. 1849)
June 9 – Samuel Slater, American industrialist (d. 1835)
June 20 – William Findlay, American politician (d. 1846)
June 30 – Elizabeth Monroe, First Lady of the United States (d. 1830)
July 4 – Adam Karl August von Eschenmayer, German philosopher (d. 1852)
July 20 – Praskovia Kovalyova-Zhemchugova, Russian serf actress and opera soprano (d. 1803)
July 27 – Charlotte Corday. French murderer of Jean-Paul Marat (d. 1793)
August 6 – Jean-Baptiste Bessières, French marshal (d. 1813)
September 4 – François-René de Chateaubriand, French writer and diplomat (d. 1848)
September 28 – Pauline Léon, French feminist and radical (d. 1838)
September 23 – William Wallace, Scottish Mathematician (d. 1843)
October 2 – William Beresford, 1st Viscount Beresford, British general and politician (d. 1854)
October 6 – Josef Madersperger, Austrian tailer and inventor, sewing machine pioneer (d. 1850)
October 31 – María Isidra de Guzmán y de la Cerda, Spanish scholar (b. 1803)
November 3 – Karađorđe Petrović, Serbs leader of the First Serbian Uprising against the Ottoman Empire, and the founder of the Serbian Karađorđević dynasty (d. 1817)
Zacharias Werner, German religious poet (d. 1823)
José Marchena Ruiz de Cueto, Spanish writer (d. 1821)
November 21 – Friedrich Schleiermacher, German theologian (d. 1834)
date unknown – Marie-Jeanne de Lalande, French astronomer and mathematician (d. 1832)
Wang Zhenyi, Chinese astronomer
Amelia Griffiths, British phycologist (d. 1858)
February 1 – Sir Robert Rich, 4th Baronet, British cavalry officer (b. 1685)
February 2 – Robert Smith, English mathematician (b. 1689)
February 8 – George Dance the Elder, English architect (b. 1695)
February 17 – Arthur Onslow, English politician (b. 1691)
March 1 – Hermann Samuel Reimarus, German philosopher and writer (b. 1694)
March 3 – Nicola Porpora, Italian composer (b. 1686)
March 18 – Laurence Sterne, Irish writer (b. 1713)
April 19 – Canaletto, Italian artist (b. 1697)
April 29 – Georg Brandt, Swedish chemist and mineralogist (b. 1694)
June 8 – Johann Joachim Winckelmann, German classical scholar and archaeologist (b. 1717)
June 15 – James Short, Scottish mathematician (b. 1710)
June 19 – Benjamin Tasker, Provincial Governor of Maryland (b. 1690)
July 6 – Conrad Beissel, German-born religious leader
July 24 – Nathaniel Lardner, English theologian (b. 1684)
August 3 – Thomas Secker, Archbishop of Canterbury (b. 1693)
August 17 (N.S.) – Vasily Trediakovsky, Russian poet (b. 1703)
September 2 – Antoine Deparcieux, French mathematician (b. 1703)
October 1 – Robert Simson, Scottish mathematician (b. 1687)
October 28 – Michel Blavet, French flutist (b. 1700)
October 31 – Francesco Maria Veracini, Italian composer (b. 1690)
November 17 – Thomas Pelham-Holles, 1st Duke of Newcastle, Prime Minister of the United Kingdom (b. 1693)
December 8 – Jean Denis Attiret, French Jesuit missionary and painter (b. 1702)
December 20 – Carlo Innocenzo Frugoni, Italian poet (b. 1692)
1768 (MDCCLXVIII) was a leap year starting on Friday (dominical letter CB) of the Gregorian calendar and a leap year starting on Tuesday (dominical letter FE) of the Julian calendar, the 1768th year of the Common Era (CE) and Anno Domini (AD) designations, the 768th year of the 2nd millennium, the 68th year of the 18th century, and the 9th year of the 1760s decade. As of the start of 1768, the Gregorian calendar was 11 days ahead of the Julian calendar, which remained in localized use until 1923.