October 13 is the 286th day of the year (287th in leap years) in the Gregorian calendar. There are 79 days remaining until the end of the year.
* 54 – Nero ascends to the Roman throne
* 409 – Vandals and Alans cross the Pyrenees and appear in Hispania.
* 1307 – Hundreds of Knights Templar in France are simultaneously arrested by agents of Phillip the Fair, to be later tortured into a "confession" of heresy.
* 1332 – Rinchinbal Khan, Emperor Ningzong of Yuan became the Khagan of the Mongols and Emperor of the Yuan Dynasty, reigning for only 53 days.
* 1362 – The Chancellor of England for the first time opened Parliament with a speech in English.
* 1582 – Because of the implementation of the Gregorian calendar, this day does not exist in this year in Italy, Poland, Portugal and Spain.
* 1773 – The Whirlpool Galaxy is discovered by Charles Messier.
* 1775 – The United States Continental Congress orders the establishment of the Continental Navy (later renamed the United States Navy).
* 1777 – After his defeat on October 7, 1777, British General John Burgoyne's Army at The Battles of Saratoga become surrounded by superior numbers, setting the stage for its surrender — which feat of arms inspires the Kingdom of France to enter the American Revolutionary War against the British.
* 1792 – In Washington, D.C., the cornerstone of the United States Executive Mansion (known as the White House since 1818) is laid.
* 1812 – War of 1812: Battle of Queenston Heights – As part of the Niagara campaign in Ontario, Canada, United States forces under General Stephen Van Rensselaer are repulsed from invading Canada by British and native troops led by Sir Isaac Brock.
* 1843 – In New York City, Henry Jones and 11 others found B'nai B'rith (the oldest Jewish service organization in the world).
* 1845 – A majority of voters in the Republic of Texas approve a proposed constitution, that if accepted by the U.S. Congress, will make Texas a U.S. state.
* 1881 – Revival of the Hebrew language as Eliezer Ben-Yehuda and friends agree to use Hebrew exclusively in their conversations.
* 1884 – Greenwich, in London, England, is established as Universal Time meridian of longitude.
* 1885 – The Georgia Institute of Technology (Georgia Tech) is founded in Atlanta, Georgia.
* 1892 – Edward Emerson Barnard discovers D/1892 T1, the first comet discovered by photographic means, on the night of October 13–14.
* 1915 – The Battle for the Hohenzollern Redoubt marks the end of the Battle of Loos in northern France, World War I.
* 1917 – The "Miracle of the Sun" is witnessed by an estimated 70,000 people in the Cova da Iria in Fátima, Portugal.
* 1918 – Mehmed Talat Pasha and the Young Turk (C.U.P.) ministry resign and sign an armistice, ending Ottoman participation in World War I.
* 1923 – Ankara replaces Istanbul as the capital of Turkey.
* 1943 – World War II: The new government of Italy sides with the Allies and declares war on Germany.
* 1944 – World War II: Riga, the capital of Latvia is seized by the Red Army.
* 1946 – France adopts the constitution of the Fourth Republic.
* 1962 – The Pacific Northwest experiences a cyclone the equal of a Cat 3 hurricane. Winds measured above 150 mph at several locations; 46 people died.
* 1967 – The first game in the history of the American Basketball Association is played as the Anaheim Amigos lose to the Oakland Oaks 134-129 in Oakland, California.
* 1970 – Fiji joins the United Nations.
* 1972 – An Aeroflot Ilyushin Il-62 crashed outside Moscow killing 176.
* 1972 – Uruguayan Air Force Flight 571 crashes in the Andes mountains, near the border between Argentina and Chile. By December 23, 1972, only 16 out of 45 people lived long enough to be rescued.
* 1976 – A Bolivian Boeing 707 cargo jet crashes in Santa Cruz, Bolivia, killing 100 (97, mostly children, killed on the ground).
* 1976 – The first electron micrograph of an Ebola viral particle was obtained by Dr. F.A. Murphy, now at U.C. Davis, who was then working at the C.D.C.
* 1977 – Four Palestinians hijack Lufthansa Flight 181 to Somalia and demand release of 11 members of the Red Army Faction.
* 1983 – Ameritech Mobile Communications (now AT&T) launched the first US cellular network in Chicago, Illinois.
* 1990 – End of the Lebanese Civil War. Syrian forces launch an attack on the free areas of Lebanon removing General Michel Aoun from the presidential palace.
* 1992 – An Antonov An-124 operated by Antonov Airlines registered SSSR-82002, crashed near Kiev, Ukraine.
* 1999 – The United States Senate rejects ratification of the Comprehensive Test Ban Treaty (CTBT).