1871 (MDCCCLXXI) was a common year starting on Sunday of the Gregorian calendar and a common year starting on Friday of the Julian calendar, the 1871st year of the Common Era (CE) and Anno Domini (AD) designations, the 871st year of the 2nd millennium, the 71st year of the 19th century, and the 2nd year of the 1870s decade. As of the start of 1871, the Gregorian calendar was 12 days ahead of the Julian calendar, which remained in localized use until 1923.

• January 2 – Amadeus I becomes King of Spain.
• January 18 – Germany becomes a unified country called the German Empire when states of the North German Confederation and south German states of the Kingdom of Bavaria, the Kingdom of Württemberg, the Grand Duchy of Baden and the Grand Duchy of Hesse-Darmstadt unite. The King of Prussia becomes the first German Emperor as Wilhelm I of Germany.
• January 10 – France surrenders (gives up) to end the Franco-Prussian War
• March 22 – In North Carolina, William Holden is the first American governor (leader of a U.S. state) to be impeached (removed from office)
• March 26 – The Paris Commune takes power in Paris.
• March 29 – The Royal Albert Hall is opened by Queen Victoria.
• April – Stockholms Handelsbank is formed.
• October 12 – The introduction of the so-called Criminal Tribes Act was enacted in British India.

• January 17 – David Earl Betty of the North Sea and of Brooksby, British admiral (navy leader) (d. 1936)
• January 30 – Wilfred Lucas, actor (d. 1940)
• February 4 – Friedrich Ebert, president of the Weimar Republic (d. 1925)
• March 5 – Rosa Luxemburg, politician (d. 1919)
• March 27 – Heinrich Mann, speaker and writer (d. 1950)
• May 6 – Christian Morgenstern, writer (d. 1914)
• May 27 – Georges Rouault, painter and artist (d. 1958).
• July 23 – Tsunesaburō Makiguchi (Japanese old Lunar calendar 6 June was an incorrect date using in Gregorian calendar), First president of Soka Gakkai International (SGI) (d. 1944).
• August 19 – Orville Wright of the Wright brothers, Americans who invented the airplane.
• August 29 – Albert Lebrun, French politician (d. 1950)
• September 27 – Grazia Deledda, Sardinian writer – Nobel prize (d. 1936)
• December 13 – Emily Carr, Canadian artist and writer.
• Richard Turner, Canadian soldier with the Royal Canadian Dragoons, who got the Victoria Cross for bravery during the Second Boer War.
• Guangxu, Emperor of the Qing Dynasty in China.

• February 20 – Paul Kane, painter
• September 23 – Louis-Joseph Papineau, aged 85, Canadian politician and leader of the Patriotes Rebellion.
• October 10 - Octavius Catto, aged 32, American black educator.
• October 18 – Charles Babbage, aged 79, English mathematician and inventor of computing machines.