January 9 – The North Carolina General Assembly authorizes nine commissioners to purchase 100 acres (0.40 km2) of land for the county seat of Chatham County. The town is named Pittsborough (later shortened to Pittsboro) for William Pitt the Younger.
January 11 – William Herschel discovers Titania and Oberon, two moons of Uranus.
January 19 – Mozart's Symphony No. 38 is premièred in Prague.
February 4 – Shays' Rebellion in Massachusetts fails.
February 28 – A charter is granted establishing the institution which will become the University of Pittsburgh.
April 2 – A Charter of Justice is signed providing the authority for the establishment of the first New South Wales (i.e. Australian) Courts of Criminal and Civil Jurisdiction.
May 7 – The New Church is founded.
May 13 – Captain Arthur Phillip leaves Portsmouth in England with the eleven ships of the First Fleet carrying around 700 convicts and at least 300 crew and guards to establish a penal colony in Australia.
May 14 – In Philadelphia, delegates begin arriving for a Constitutional Convention.
May 22 – In Britain, Thomas Clarkson and Granville Sharp found the Society for Effecting the Abolition of the Slave Trade with support from John Wesley, Josiah Wedgwood and others.
May 25 – In Philadelphia, delegates begin to convene the Constitutional Convention intended to amend the Articles of Confederation. However, a new United States Constitution is eventually produced. George Washington presides over the Convention.
May – Orangist troops attack Vreeswijk, Harmelen and Maarssen: civil war starts in the Dutch Republic.
May 31 – The original Lord's Cricket Ground in London holds its first cricket match; Marylebone Cricket Club founded.
June 20 – Oliver Ellsworth moves at the Federal Convention that the government be called the United States.
June 28 – Princess Wilhelmina of Orange, sister of King Frederick William II of Prussia, is captured by Dutch Republican patriots, taken to Goejanverwellesluis and not allowed to travel to The Hague.
July 13 – The Congress of the United States enacts the Northwest Ordinance establishing governing rules for the Northwest Territory. It also establishes procedures for the admission of new states and limits the expansion of slavery.
August 27 – Launching a 45-foot (14 m) steam powered craft on the Delaware River, John Fitch demonstrates the first U.S. patent for his design.
September 13 – Prussian troops invade the Dutch Republic. Within a few weeks 40,000 Patriots (out of a population of 2,000,000) go into exile in France (and learn from observation the ideals of the French Revolution).
September 17 – The United States Constitution is adopted by the Constitutional Convention in Philadelphia.
September 24 – Washington Academy (later Washington & Jefferson College) is chartered by the Pennsylvania General Assembly.
October 1 – Russo-Turkish War (1787–92) – Battle of Kinburn: Alexander Suvorov, though sustaining a wound, routs the Turks.
October 27 – The first of The Federalist Papers, a series of essays calling for ratification of the U.S. Constitution, is published in The Independent Journal, a New York newspaper.
October 29 – Wolfgang Amadeus Mozart's opera Don Giovanni (libretto by Lorenzo Da Ponte) premieres in the Estates Theatre in Prague.
November 1 – The first secondary education school open to girls in Sweden, Societetsskolan, is founded in Gothenburg.
December 3 – James Rumsey demonstrates his water-jet propelled boat on the Potomac River.
December 7 – Delaware ratifies the Constitution and becomes the first U.S. state.
December 8 – La Purisima Mission is founded by Padre Fermín Lasuén as the eleventh of the Spanish missions in California.
December 12 – Pennsylvania becomes the second U.S. state.
December 18 – New Jersey becomes the third U.S. state.
December 23 – Captain William Bligh sets sail from England for Tahiti in HMS Bounty.
Caroline Herschel is granted an annual salary of £50 by King George III of Great Britain for acting as assistant to her brother William in astronomy.
The North Carolina General Assembly incorporates Waynesborough, and designates it the county seat for Wayne County, North Carolina.
Antoine Lavoisier is the first to suggest that silica is an oxide of a hitherto unknown metallic chemical element, later isolated and named silicon.
Freed slave Ottobah Cugoano publishes Thoughts and Sentiments on the Evil and Wicked Traffic of the Slavery and Commerce of the Human Species in England.
January 1 – Manuel José Arce, Revolutionary General and first President of The Federal Republic of Central America. (d. 1847)
February 10 – William Bradley, Britain's tallest man ever 7 ft 9 in. (d. 1820)
February 17 – George Mogridge (Old Humphrey), English writer and poet (d. 1854)
March 6 – Joseph von Fraunhofer, German optician (d. 1826)
March 7 – George Bethune English, American explorer and writer (d. 1828)
March 9 - Josephine Kablick, Czech botanist and paleontologist (d. 1863)
March 11 – Ivan Nabokov, Russian General (d. 1852)
April 26 – Ludwig Uhland, German poet (d. 1862)
June 28 – Sir Harry Smith, English soldier and military commander (d. 1860)
August 24 – James Weddell, British sailor known for discovering the Weddell Sea (d. 1834)
September 5 – François Sulpice Beudant, French mineralogist and geologist (d. 1850)
October 20 – Úrsula Goyzueta, Bolivian heroine (d. 1854)
November 4 – Edmund Kean, English actor (d. 1833)
November 7 – Vuk Stefanović Karadžić, Serbian linguist and major reformer of the Serbian language (d. 1864)
November 18 – Louis Daguerre, French artist and chemist (d. 1851)
November 21 – Samuel Cunard, Canadian business, prominent Nova Scotian, founder of the Cunard Line (d. 1865)
November 25 – Franz Xaver Gruber, Austrian composer (d. 1863)
December 10 – Thomas Hopkins Gallaudet, American educator (d. 1851)
December 11 – Macacha Güemes, Argentine heroine (d. 1866)
December 16 – Mary Russell Mitford, English novelist and dramatist (d. 1855)
December 17 – Jan Evangelista Purkyne, Czech anatomist and botanist (d. 1869)
Hugh Maxwell, American lawyer and politician (d. 1873)
Juana Galán, Spanish heroine (d. 1812)
Rudjer Boscovich, Croatian scientist and diplomat (b. 1711)
Charles Gravier, comte de Vergennes, French statesman and diplomat (b. 1717)
April 1 – Floyer Sydenham, English classical scholar (b. 1710)
April 2 – Thomas Gage, British general (b. 1719)
May 10 – William Watson, English physician and scientist (b. 1715)
May 28 – Leopold Mozart, Austrian composer (b. 1719)
June 20 – Carl Friedrich Abel, German composer (b. 1723)
July 4 – Charles, Prince of Soubise, Marshal of France (b. 1715)
August 1 – Alphonsus Maria de' Liguori, Italian founder of the Redemptionist order (b. 1696)
October 7 – Henry Muhlenberg, German-born founder of the U.S. Lutheran Church (b. 1711)
October 28 – Johann Karl August Musäus, German author (b. 1735)
November 3 – Robert Lowth, English bishop and grammarian (b. 1710)
November 15 – Christoph Willibald Gluck, German composer (b. 1714)
December 18 – Soame Jenyns, English writer (b. 1704)
Francis William Drake, British admiral and Governor of Newfoundland (b. 1724)
Maria Antonia Fernandez, Spanish flamenco singer and dancer (b. 1751)
The Two-Headed Boy of Bengal who suffered from a rare condition called Craniopagus parasiticus (b. 1783)
1787 (MDCCLXXXVII) was a common year starting on Monday (dominical letter G) of the Gregorian calendar and a common year starting on Friday (dominical letter C) of the Julian calendar, the 1787th year of the Common Era (CE) and Anno Domini (AD) designations, the 787th year of the 2nd millennium, the 87th year of the 18th century, and the 8th year of the 1780s decade. As of the start of 1787, the Gregorian calendar was 11 days ahead of the Julian calendar, which remained in localized use until 1923.