June 1 – American Revolutionary War – Benedict Arnold is court-martialed for malfeasance, in his treatment of government property.
June 16 – American Revolutionary War – In support of the U.S., Spain declares war on Britain.
July 24 – American Revolutionary War – American forces, led by Commodore Dudley Saltonstall, launch the Penobscot Expedition in what is now Castine, Maine, resulting in the worst naval defeat in U.S. history (until Pearl Harbor).
September 23 – American Revolutionary War – Battle of Flamborough Head – The American ship Bonhomme Richard, commanded by John Paul Jones, engages the British ship HMS Serapis. The Bonhomme Richard sinks, but the Americans board the Serapis and other vessels, and are victorious.
December 29 – American Revolutionary War: Capture of Savannah – British forces under Archibald Campbell take the city of Savannah, Georgia.
January 14 – The University of North Carolina opens to students at Chapel Hill, becoming the first state university in the United States.
February 7 – The Eleventh Amendment to the United States Constitution is passed.
May 1 – Unification of Hawai‘i: Battle of Nuʻuanu: Kamehameha I of the Island of Hawaii defeats the Oahuans, solidifying his control of the major islands of the archipelago and officially founding the Kingdom of Hawaii.
October 20 – The United States signs a treaty with Spain, opening commerce along the Mississippi River to the Gulf of Mexico, and establishing boundaries between U.S. territory and Spanish Florida.
November 2 – French Revolution: The French Directory takes power; the influence of the Sans-culottes declines.
undated: Jim Beam is founded as Old Jake Beam Sour Mash.
January 5 – The United States House of Representatives votes to stop sharing the Oregon Country with the United Kingdom.
February 4 – Many Mormons begin their migration west from Nauvoo, Illinois, to the Great Salt Lake, led by Brigham Young.
February 19 – United States president James K. Polk's annexation of the Republic of Texas is finalized by Texas president Anson Jones in a formal ceremony of transfer of sovereignty. The newly formed Texas state government is officially installed in Austin.
February 26 – The Liberty Bell in Philadelphia is cracked while being rung for George Washington's birthday.
April 25 – Mexican–American War: Open conflict begins, over the disputed border of Texas.
May – The Associated Press is founded in New York.
May 13 – Mexican–American War: The United States declares war on Mexico.
June 10 – Mexican–American War: The California Republic declares independence from Mexico.
June 14 – Bear Flag Revolt: American settlers in Sonoma, California, start a rebellion against Mexico and proclaim the California Republic. (if you ever wondered why California has a bear on the state flag)
June 15 - The Oregon Treaty establishes the 49th parallel as the border between the United States and Canada, from the Rocky Mountains to the Strait of Juan de Fuca.
June 28 – The saxophone is patented by Adolphe Sax.
July 7 – Mexican–American War – Battle of Monterey: Acting on instructions from Washington, D.C., Commodore John Drake Sloat orders his troops to occupy Monterey and Yerba Buena, thus beginning the United States annexation of California.
August – Canadian physician and geologist Abraham Pineo Gesner demonstrates a process to refine a liquid fuel, which he calls kerosene, from coal, bitumen or oil shale.
September 10 – Elias Howe is awarded the first United States patent for a sewing machine, using a lockstitch design
September 23 – Discovery of Neptune: The planet is observed for the first time by German astronomers Johann Gottfried Galle and Heinrich Louis d'Arrest, as predicted by British astronomer John Couch Adams and French astronomer Urbain Le Verrier.
November 4 – The Donner Party, a wagon train of 87 settlers traveling to California, is stranded in the Sierra Nevada mountains by the first of several snowstorms. By the time a relief party reaches the starving settlers three months later, only 48 survivors are left, many of whom have survived by cannibalism.
December 27 – Iowa is admitted as the 29th U.S. state.
The Great Famine continues in Ireland. The first deaths from hunger take place early in the year and Phytophthora infestans almost totally destroys the summer potato crop.
January 1 – The hymn that becomes known as Amazing Grace, at this time titled "1 Chronicles 17:16–17", is first used to accompany a sermon led by curate John Newton in the town of Olney, Buckinghamshire, England.
April 27 – The Parliament of Great Britain passes the Tea Act (coming into force on May 10), designed to save the British East India Company by granting it a monopoly on the North American tea trade. [here's a hint: they shouldn't have done that]
September 11 – The Public Advertiser publishes a satirical essay titled Rules By Which A Great Empire May Be Reduced To A Small One, written by Benjamin Franklin.
October 12 – America's first insane asylum opens, for Persons of Insane and Disordered Minds, in Williamsburg, Virginia.
November 10 – Four ships— the Dartmouth, the Eleanor, the Beaver and the William— depart Britain for America, carrying the first Indian tea to be subject to the newly enacted taxes. The William is lost in a storm; the Dartmouth is the first ship to reach Boston, docking on November 28.
December 16 – Boston Tea Party: A group of American colonists, dressed as Mohawk Indians, steal aboard ships of the East India Company and dump their cargo of tea into Boston Harbor, in protest against British tax policies.
Date Unknown - In China, written work begins on the Siku Quanshu, the largest literary compilation of books in China's history (surpassing the Yongle Encyclopedia of the 15th Century). Upon completion in 1782, the books are bound in 36,381 volumes (册) with more than 79,000 chapters (卷), comprising about 2.3 million pages, and approximately 800 million Chinese characters.