July 3 - Anna Maria Pertl Mozart, mother of Wolfgang Amadeus Mozart (b. 1720)
January 18 - James Cook is the first known European to discover the Hawaiian Islands, which he names the "Sandwich Islands".
February 5 - South Carolina becomes the first state to ratify the Articles of Confederation.
February 6 - American Revolutionary War: In Paris the Treaty of Alliance and the Treaty of Amity and Commerce are signed by the United States and France signaling official recognition of the new republic.
February 14 - The United States Flag is formally recognized by a foreign naval vessel for the first time, when French Admiral Toussaint-Guillaume Picquet de la Motte rendered a nine gun salute to USS Ranger, commanded by John Paul Jones.
February 23 - American Revolution: Baron von Steuben arrives at Valley Forge, Pennsylvania to help to train the Continental Army.
March 4 - The Continental Congress voted to ratify both the Treaty of Amity and Commerce and the Treaty of Alliance with France. The two treaties were the first entered into by the United States government.
May 1 - American Revolution: The Battle of Crooked Billet begins in Hatboro, Pennsylvania.
June 18 - American Revolutionary War: British troops abandon Philadelphia, Pennsylvania.
June 28 - American Revolutionary War: Battle of Monmouth fought between the American Continental Army under George Washington and the British Army led by Sir Henry Clinton. Washington appoints Molly Pitcher a sergeant.
July 3 - American Revolutionary War: British forces massacre 360 men, women and children in the Wyoming Valley massacre.
July 4 - American Revolutionary War: Forces under George Rogers Clark capture Kaskaskia during the Illinois campaign.
July 10 - American Revolution: Louis XVI of France declares war on the Kingdom of Great Britain.
July 27 - American Revolution: First Battle of Ushant
August 26 - The first recorded ascent of Triglav, the highest mountain in Slovenia.
September 17 - The Treaty of Fort Pitt is signed. It is the first formal treaty between the United States and a Native American tribe (the Lenape or Delaware Indians).
September 19 - The Continental Congress passes the first budget of the United States.
October 3 - British Captain James Cook anchors in Alaska.
November 11 - Cherry Valley Massacre: an attack by Loyalists and Seneca Indian forces on a fort and village in eastern New York during the American Revolutionary War, killing more than forty civilians and soldiers.
November 26 - In the Hawaiian Islands, Captain James Cook becomes the first European to visit Maui.
December 29 - American Revolutionary War: 3,500 British soldiers under the command of Lieutenant Colonel Archibald Campbell captures Savannah, Georgia without firing a shot.