January 1 – Paying of old age pensions begins in Germany.
January 5 – Beginning of the Australian shearers' strike that leads indirectly to the foundation of the Australian Labor Party.
January 16 – The Chilean Civil War of 1891 breaks out.
January 20 – Jim Hogg becomes the first native Texan to be governor of that state.
January 27–May 2 – Jamaica International Exhibition.
January 29 – Liliuokalani is proclaimed Queen of Hawaii.
January 31 – The Portuguese republican revolution breaks out in the northern city of Porto.
February – Beginning of the Tobacco Protest in Iran.
February 14 – In the FA Cup quarter final in English Association football, a goal is deliberately stopped by handball on the goal line. An indirect free kick is awarded, since the penalty kick, proposed the previous year by William McCrum, has not yet been implemented. This event probably changes public opinion on the penalty kick, seen previously as 'an Irishman's motion'.
February 15 – Allmänna Idrottsklubben (AIK) sports club is founded in Stockholm, Sweden.
February 21 – Springhill, Nova Scotia, suffers a serious mining disaster.
March 3 – The International Copyright Act of 1891 is passed by the 51st United States Congress.
March 9–12 – The Great Blizzard of 1891 in the south and west of England leads to extensive snow drifts and powerful storms off the south coast, with 14 ships sunk and approximately 220 deaths attributed to the weather conditions.
March 12 – Djurgårdens IF (DIF) sports club is founded in Stockholm.
March 14 – In New Orleans, a lynch mob storms the Old Parish Prison and lynches 11 Italians arrested but found innocent of the murder of Police Chief David Hennessy.
March 15 – Jesse W. Reno patents the first escalator at Coney Beach.
March 17 – The British steamship SS Utopia, carrying Italian migrants to New York, sinks in the inner harbor of Gibraltar after collision with the battleship HMS Anson, killing 564.
March 18 – Official opening of the London–Paris telephone system.
The Wrigley Company is founded in Chicago.
The London–Paris telephone system is opened to the general public.
April 5 – Census in the United Kingdom: 15.6 million people live in cities of 20,000 or more in England and Wales and cities of 20,000 or more account for 54% of the total English population.
May – Mirza Ghulam Ahmad claims to be the Promised Messiah (the second coming of Jesus) and the Mahdi awaited in Islam.
Troops fire on a workers' May Day demonstration in support of the 8-hour workday in Fourmies, France, killing 9 and wounding 30.
The first Fascio dei lavoratori (Workers League) is founded by Giuseppe De Felice Giuffrida in Catania, Sicily.
May 5 – The Music Hall in New York (later known as Carnegie Hall) has its grand opening and first public performance, with Tchaikovsky as guest conductor.
May 11 – Ōtsu incident: Tsesarevich Nikolay Alexandrovich (the future Czar Nicholas II) of Russia survives an assassination attempt while visiting Japan.
May 15 – Pope Leo XIII issues the encyclical Rerum novarum on the rights and duties of capital and labor, resulting in the creation of many Christian Democrat parties throughout Europe.
May 20 – Thomas Edison's prototype kinetoscope is first displayed at Edison's Laboratory, for a convention of the National Federation of Women's Clubs.
May 31 N.S. (May 19 O.S.) – In the Kuperovskaya district of Vladivostok, a grand ceremonial inauguration of construction work on the Trans-Siberian Railway is carried out by the Tsesarevich Nikolay Alexandrovich and a religious service held.
June 1 – The Johnstown Inclined Plane opens in Johnstown, Pennsylvania.
June 16 – John Abbott becomes Canada's third prime minister.
June 21 – First long-distance transmission of alternating current by the Ames power plant near Telluride, Colorado, by Lucien and Paul Nunn.
June 25 – Arthur Conan Doyle's detective Sherlock Holmes appears in The Strand Magazine (London) for the first time, in the issue dated July.
July 10 – Erik Gustaf Boström becomes Prime Minister of Sweden.
July 30 – The Springboks rugby union team of South Africa play their first international test match against the Lions team of the British Isles and win by 4-0.
August 27 – France and Russia conclude a defensive alliance.
September 14 – The first penalty kick is awarded in a football (soccer) match; John Heath scores it for the Wolverhampton Wanderers.
September 28 – The C.A. Peñarol is founded in Montevideo under the name of the CURCC (Central Uruguay Railway Cricket Club).
October – Eugène Dubois finds the first fragmentary bones of Pithecanthropus erectus (later redesignated Homo erectus), or 'Java Man', at Trinil on the Solo River.
October 1 – Stanford University in California opens its doors.
October 28 – The 8.0 Ms Mino–Owari earthquake strikes the Gifu region of Japan. This oblique-slip event killed over 7,200, injured more than 17,000, and created fault scarps that still remain visible.
November 11 – Jindandao Incident breaks out: The Chinese Juu Uda League in Inner Mongolia, massacres tens of thousands of Mongols before being suppressed by government troops in late December.
November 15 – The constitution of the First Brazilian Republic is promulgated.
November 28 – The International Brotherhood of Electrical Workers is organized in St. Louis, Missouri.
December 17 – Drexel University is inaugurated as the Drexel Institute of Art, Science and Industry in Philadelphia.
December 22 – Asteroid 323 Brucia becomes the first asteroid discovered using photography.
Brahmin teacher and nationalist Bal Gangadhar Tilak begins agitation for Indian Home Rule.
New Scotland Yard becomes the HQ of the London Metropolitan Police.
James Naismith invents basketball.
Seattle University is established as the Immaculate Conception school.
The Auckland University Students' Association is founded.
Maria Skłodowska (later Marie Curie) enters the Sorbonne University.
Nikola Tesla invents the Tesla coil.
Michelin patent the removable pneumatic bicycle tire.
Skansen is established as the world's first open-air museum by Artur Hazelius on the island of Djurgården in Stockholm, Sweden.
The 1891 census of India is conducted.
First production of the Swiss Army Knife by Victorinox begins.
January 1 – Charles Bickford, American actor (d. 1967)
January 2 – Charles P. Thompson, American actor (d. 1979)
January 7 – Zora Neale Hurston, Harlem Renaissance writer (d. 1960)
January 8 – Walther Bothe, German physicist, Nobel Prize in Physics (d. 1957)
Antonio Gramsci, Italian Communist writer and politician (d. 1937)
Bruno Loerzer, German aviator and air force general (d. 1960)
January 24 – Walter Model, German field marshal (d. 1945)
January 27 – Ilya Ehrenburg, Russian writer (d. 1967)
February 2 – Antonio Segni, Italian politician who was the 34th Prime Minister of Italy (1955–1957, 1959–1960), and the fourth President of the Italian Republic (d. 1972)
February 9 – Ronald Colman, English actor (d. 1958)
February 11 – J. W. Hearne, English cricketer (d. 1965)
February 13 – Grant Wood, American painter (d. 1942)
February 15 – Henry J. Knauf, American politician (d. 1950)
February 17 – Abraham Fraenkel, German-born Israeli mathematician and recipient of the Israel Prize (d. 1965)
February 21 – Seán Heuston, Irish rebel (d. 1916)
February 27 – David Sarnoff, Russian-born American broadcasting pioneer (d. 1971)
March 3 – Fritz Rumey, German World War I fighter ace (d. 1918)
March 9 – José P. Laurel, 3rd President of the Philippines (d. 1959)
March 10 – Sam Jaffe, American actor (d. 1984)
March 16 - Patsy Gallacher, Irish footballer (d. 1953)
March 19 – Earl Warren, American politician and Chief Justice of the United States (d. 1974)
March 24 – Rudolf Berthold, German fighter pilot (d. 1920)
March 26 – Will Wright, American actor (d. 1962)
March 29 – Yvan Goll, French lyricist and dramatist (d. 1950)
April 2 – Max Ernst, German painter (d. 1976)
Ole Kirk Christiansen, founder of the Lego group (d. 1958)
Minoru Ōta, Japanese admiral (d. 1945)
April 13 – Nella Larsen, American novelist (d. 1964)
April 14 – B. R. Ambedkar, One of the founding fathers of modern India and the architect of its constitution (d. 1956)
Väinö Raitio, Finnish composer (d. 1945)
Wallace Reid, American actor (d. 1923)
April 17 – George Adamski, Polish-born alleged UFO traveler (d. 1965)
April 20 – Aldo Finzi, Italian politician (d. 1944)
April 23 – Sergei Prokofiev, Soviet composer (d. 1953)
April 29 – Bharathidasan, 20th-century Tamil poet and rationalist (d. 1964)
May 7 – Harry McShane, Scottish socialist (d. 1988)
Anton Dostler, German general (d. 1945)
Mahmoud Mokhtar, Egyptian sculptor (d. 1934)
Mikhail Bulgakov, Russian writer (d. 1940)
Fritz Feigl, Austrian-born chemist (d. 1971)
Richard Tauber, Austrian tenor (d. 1948)
Adolf Ritter von Tutschek, German fighter ace (d. 1918)
May 18 – Rudolf Carnap, German philosopher (d. 1970)
May 19 – Oswald Boelcke, German World War I fighter ace (d. 1916)
May 22 – Eddie Edwards, American jazz trombonist (d. 1963)
May 23 – Pär Lagerkvist, Swedish writer, Nobel Prize laureate (d. 1974)
May 24 – William F. Albright, American archeologist and Biblical scholar (d. 1971)
May 26 – Paul Lukas, Hungarian-born American actor (d. 1971)
June 2 – Takijirō Ōnishi, Japanese admiral (d. 1945)
June 3 – Jim Tully, vagabond, pugalist, noted American writer (d. 1947 heart disease)
June 9 – Cole Porter, American composer and songwriter (d. 1964)
June 20 – John A. Costello, second President of Ireland (d. 1976)
June 21 – Hermann Scherchen, German conductor (d. 1966)
Esther Forbes, American writer (d. 1967)
Carl Andrew Spaatz, American general (d. 1974)
June 30 – Man Mountain Dean, American professional wrestler (d. 1953)
July 2 – Karin Kock-Lindberg, Swedish politician (d. 1976)
July 5 – John Howard Northrop, American chemist, Nobel Prize laureate (d. 1987)
July 7 – Tadamichi Kuribayashi, Imperial Japanese Army general (d. 1945)
July 11 – Joseph Sadi-Lecointe, French aviator (d. 1944)
July 21 – Elmer Ripley, American basketball coach (d. 1982)
July 26 – William J. Connors, American politician (d. 1961)
July 27 – Jacob van der Hoeden, Dutch-Israeli veterinary scientist (d. 1968)
July 29 – Bernhard Zondek German-born Israeli gynecologist, developer of first reliable pregnancy test (d. 1966)
July 30 – Roderic Dallas, Australian World War I fighter ace (d. 1918)
August 2 – Viktor Maksimovich Zhirmunsky, Russian literary historian, linguist (d. 1971)
August 11 – Stancho Belkovski, Bulgarian architect and lecturer (d. 1962)
August 21 – Emiliano Mercado del Toro, Puerto Rican, longest-lived war veteran ever and last verified person born in 1891 (d. 2007)
August 25 – David Shimoni, Russian-born Israeli poet and writer (d. 1956)
September 3 – Bessie Delany, African American physician and author (d. 1995)
September 5 – Edward Molyneux, English fashion designer (d. 1974)
September 12 – Pedro Albizu Campos, advocate of Puerto Rican independence (d. 1965)
September 14 – William F. Friedman, American cryptographer (d. 1969)
Teruo Akiyama, Japanese admiral (d. 1943)
Karl Dönitz, German admiral and briefly President of Germany (d. 1980)
Stephanie von Hohenlohe, Austrian-born German World War II spy (d. 1972)
Julie Winnefred Bertrand, Canadian supercentenarian (d. 2007)
September 18 – Rafael Pérez y Pérez, Spanish writer (d. 1984)
September 22 – Hans Albers, German actor and singer (d. 1960)
September 26 – Charles Munch, French conductor and violinist (d. 1968)
September 28 – Myrtle Gonzalez, American film and stage actress (d. 1918)
October 12 – Fumimaro Konoe, Prime Minister of Japan (d. 1945)
October 17 – Yasuyo Yamasaki, Imperial Japanese Army officer (d. 1943)
October 20 – James Chadwick, English physicist, Nobel Prize laureate (d. 1974)
October 24 – Rafael Trujillo, dictator of the Dominican Republic (d. 1961)
October 25 – Charles Coughlin, American antisemitic radio host and Catholic priest (d. 1979)
October 28 – Ormer Locklear, American stunt pilot and film actor (d. 1920)
November 2 – David Townsend, American art director (d. 1935)
November 4 – Orlando Ward, American general (d. 1972)
November 7 – Miriam Cooper, American silent film actress (d. 1976)
November 10 – Carl Stalling, American musician (d. 1972)
November 14 – Frederick Banting, Canadian physician, recipient of the Nobel Prize in Physiology or Medicine (d. 1941)
Vincent Astor, American philanthropist (d. 1959)
Erwin Rommel, German field marshal (d. 1944)
November 28 – Gregorio Perfecto, Filipino jurist & politician (d. 1949)
November 29 – Julius Raab, former Chancellor of Austria (d. 1964)
December 4 – T. V. Soong, Republic of China businessman and politician (d. 1971)
Masatomi Kimura, Japanese admiral (d. 1960)
Gotthard Sachsenberg, German World War I naval aviator and fighter ace (d. 1961)
December 9 – Maksim Bahdanovič, Belarusian poet (d. 1917)
Harold Alexander, 1st Earl Alexander of Tunis, British field marshal (d. 1969)
Nelly Sachs, German writer, Nobel Prize laureate (d. 1970)
Katherine MacDonald, American silent screen actress (d. 1956)
Lester Melrose, American record producer, known primarily for promoting the Chicago blues genre (d. 1968)
Karl Emil Schäfer, German World War I fighter ace (d. 1917)
Hu Shih, Chinese liberal (d. 1962)
December 19 – Edward Bernard Raczynski, former President of Poland (d. 1993)
December 24 – Feodor Stepanovich Rojankovsky, Russian illustrator (d. 1970)
Kenneth Arthur Noel Anderson, British general (d. 1959)
Clarrie Grimmett, New Zealand-Australian cricketer (d. 1980)
December 26 – Henry Miller, American writer (d. 1980)
Godfrey Ince, British civil servant (d. 1960)
W. Alton Jones, American industrialist and philanthropist (d. 1962)
Anna Sprengel, German Countess (alleged death)
January 5 – Emma Abbott, American opera singer (b. 1849)
January 16 – Léo Delibes, French composer (b. 1836)
January 20 – Kalākaua, last reigning King of Hawaii (b. 1836)
Calixa Lavallée, Canadian composer (b. 1842)
James Timberlake, American lawman (b. 1846)
January 26 – Nikolaus Otto, German engineer (b. 1832)
February 13 – David Dixon Porter, American admiral (b. 1813)
February 14 – William Tecumseh Sherman, American general (b. 1820)
Théodore de Banville, French writer (b. 1823)
Sir Joseph Bazalgette, English civil engineer (b. 1819)
March 29 – Georges Seurat, French painter (b. 1859)
April 2 – Ahmed Vefik Pasha, Turkish statesman (b. 1823)
April 7 – P. T. Barnum, American showman (b. 1810)
April 9 – George Cavendish-Bentinck, British Conservative politician (b. 1821)
April 24 – Helmuth von Moltke the Elder, Prussian field marshal (b. 1800)
April 25 – Nathaniel Woodard, educationalist (b. 1811)
May 4 – Professor James Moriarty, fictional criminal mastermind of Sir Arthur Conan Doyle's Sherlock Holmes short story The Final Problem (b. unknown)
May 8 – Helena Blavatsky, Russian-born author and theosophist (b. 1831)
June 6 – John A. Macdonald, 1st Prime Minister of Canada and Father of Confederation (b. 1815)
June 19 – David Settle Reid, American politician (b. 1813)
June 23 – Samuel Newitt Wood, American politician (b. 1825)
June 24 – Wilhelm Eduard Weber, German physicist (b. 1804)
July 4 – Hannibal Hamlin, 15th Vice President of the United States (b. 1809)
July 24 – Hermann Raster, German Forty-Eighter and Editor in Chief of the Illinois Staats-Zeitung (b. 1827)
August 12 – James Russell Lowell, American poet and essayist (b. 1819)
August 14 – Sarah Childress Polk, First Lady of the United States (b. 1803)
August 27 – Samuel C. Pomeroy, American politician and railroad executive (b. 1816)
August 29 – Pierre Lallement, French inventor of the bicycle (b. 1843?)
September 7 – Lorenzo Sawyer, 9th Chief Justice of the Supreme Court of California (b. 1820)
September 11 – Antero de Quental, Portuguese poet (b. 1842)
September 15 – Ivan Goncharov, Russian author (b. 1812)
September 28 – Herman Melville, American novelist (b. 1819)
September 30 – Georges Ernest Boulanger, French general and politician (b. 1837)
Charles I of Württemberg (b. 1823)
Charles Stewart Parnell, Irish nationalist leader (b. 1846)
October 15 – Gilbert Arthur à Beckett, English writer (b. 1837)
October 23 – Ambrose of Optina, Russian Orthodox saint (b. 1812)
October 25 – Prince Kuni Asahiko (b. 1824)
October 29 – Prince Yamashina Akira (b. 1816)
November 6 – J. Gregory Smith, Vermont governor (b. 1818)
November 10 – Arthur Rimbaud, French poet (b. 1854)
November 17 – George H. Cooper, United States Navy admiral (b. 1821)
November 28 – Sir James Corry, 1st Baronet, British politician (b. 1826)
December 5 – Pedro II, Brazilian deposed emperor (b. 1825)
December 29 – Leopold Kronecker, Polish-German mathematician and academic (b. 1823)
December 31 – Samuel Ajayi Crowther, 1st African Anglican bishop; linguist and legendary missionary (b. 1809)
William Robert Woodman, British co-founder of the Hermetic Order of the Golden Dawn (b. 1828)
1891 (MDCCCXCI) was a common year starting on Thursday (dominical letter D) of the Gregorian calendar and a common year starting on Tuesday (dominical letter F) of the Julian calendar, the 1891st year of the Common Era (CE) and Anno Domini (AD) designations, the 891st year of the 2nd millennium, the 91st year of the 19th century, and the 2nd year of the 1890s decade. As of the start of 1891, the Gregorian calendar was 12 days ahead of the Julian calendar, which remained in localized use until 1923.