• Beginning of the Irish potato famine.
• James Knox Polk succeeds John Tyler as President of the United States of America
• January 29 - The Raven by Edgar Allan Poe is published for the first time (New York Evening Mirror[?]).
• March 1 - President John Tyler signs a bill authorizing the United States to annex the Republic of Texas.
• March 3 - Florida is admitted as the 27th U.S. state.
• March 3 - For the first time the United States Congress passes legislation overriding a presidential veto.
• March 11 - First maori War[?]: Chiefs Kawiti[?] and Hone-Heke[?] leads 700 Maoris in the burning of the white settlement of Kororareka[?], now known as Russel.
• May 20 - The HMS Erebus and Terror with 134 men under John Franklin[?] sail from the River Thames beginning a disastrous expedition to find the Northwest Passage.
• July 4 - Near Concord, Massachusetts, Henry David Thoreau embarks on a two-year experiment in simple living at Walden Pond[?] (see Walden[?]).
• August 28 - Scientific American begins publication
• Second separation of Republic of Yucatan from Mexico
• December 27 - Anesthesia is used for childbirth for the first time (Dr. Crawford Williamson Long[?] in Jefferson, Georgia).
• December 29 - Texas is admitted as the 28th U.S. state.

Arts, Sciences, Literature and Philosophy

• 1845 in literature:
  • The Count of Monte Cristo - Alexandre Dumas, père
• 1845 in music:
• 1845 in sports:

Births

• January 7 - King Ludwig II of Bavaria (+ 1921)
• March 3 - Georg Cantor, German mathematician (+ 1918)
• March 10 - Emperor Alexander III of Russia
• March 27 - Wilhelm Conrad Röntgen, physicist, winner of the first Nobel Prize in physics 1901 (+ 1923)
• May 12 - Gabriel Fauré, composer (+ 1924)
• May 30 - King Amadeus I of Spain
• Jacint Verdaguer, Catalan poet
• John Sparrow David Thompson, Canadian prime minister.
• Wilhelm Conrad Roentgen[?], Prussian physicist.

Deaths

• May 12 - Janos Bacsanyi, Hungarian poet
• Andrew Jackson, USA general and president