1845 (MDCCCXLV) was a common year starting on Wednesday of the Gregorian calendar and a common year starting on Monday (dominical letter G) of the Julian calendar, the 1845th year of the Common Era (CE) and Anno Domini (AD) designations, the 845th year of the 2nd millennium, the 45th year of the 19th century, and the 6th year of the 1840s decade. As of the start of 1845, the Gregorian calendar was 12 days ahead of the Julian calendar, which remained in localized use until 1923.
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- January 10 – Elizabeth Barrett receives a love letter from the younger poet Robert Browning on May 20 they meet for the first time in London. She begins writing her Sonnets from the Portuguese.
- January 23 – The United States Congress establishes a uniform date for federal elections, which will henceforth be held on the first Tuesday after the first Monday in November.
- January 29 – "The Raven" by Edgar Allan Poe is published for the first time (New York Evening Mirror).
- February 1 – Anson Jones, President of the Republic of Texas, signs the charter officially creating Baylor University. Baylor is the oldest university in the State of Texas operating under its original name.
- February 7 – In the British Museum, a drunken visitor smashes the Portland Vase, which takes months to repair.
- February 28 – The United States Congress approves the annexation of Texas.
- March 1 – President John Tyler signs a bill authorizing the United States to annex the Republic of Texas.
- March 3
- March 4 – James K. Polk is sworn in as the 11th President of the United States.
- March 11 – New Zealand Wars open with the Flagstaff War: Chiefs Kawiti and Hone Heke lead 700 Māoris in the burning of the British colonial settlement of Kororāreka (modern-day Russell, New Zealand).
- March 13 – The Violin Concerto by Felix Mendelssohn premieres in Leipzig, with Ferdinand David as soloist.
- March 17 – Stephen Perry patents the rubber band in the United Kingdom.
- March 30 – Due to different transition dates to the Gregorian calendar, Finland (then part of the Russian Empire) is the only place in the world to have Easter day on this particular Sunday.
- April 10 – A great fire destroys much of the American city of Pittsburgh.
- April 20 – Ramón Castilla becomes president of Peru.
- May – Frederick Douglass's Narrative of the Life of Frederick Douglass, an American Slave written by himself is published by the Boston Anti-Slavery Society.
- May 2 – A suspension bridge collapses in Great Yarmouth, England, leaving around 80 dead, mostly children.
- May 19 – HMS Erebus and HMS Terror with 134 men, comprising Sir John Franklin's expedition to find the Northwest Passage, sail from Greenhithe on the Thames. They will last be seen in August entering Baffin Bay.
- May 30 – Fatel Razack (Fath Al Razack, "Victory of Allah the Provider", Arabic: قتح الرزاق) is the first ship to bring indentured labourers from India to Trinidad and Tobago, landing in the Gulf of Paria with 227 immigrants.
- June 8— Andrew Jackson dies.
- July 20 – Charles Sturt enters the Simpson Desert in central Australia.
- July 26–August 10 – Isambard Kingdom Brunel's iron steamship Great Britain makes the transatlantic crossing from Liverpool to New York, the first screw propelled vessel to make the passage.
- July 28 – HMS Terror and HMS Erebus of the Franklin Expedition go missing in the Davis Strait west of Greenland while searching for the Northwest Passage.
- August 9 – The Aberdeen Act is passed by the Parliament of the United Kingdom empowering the British Royal Navy to search Brazilian ships as part of the abolition of the slave trade from Africa.
- August 10 – The French Consul in Zanzibar (M. Broquant) receives the final letter sent by Eugène Maizan during his expedition into tropical Africa.
- August 28 – The journal Scientific American begins publication.
- September 9 – Potato blight breaks out in Ireland: beginning of the Great Famine.
- September 18 – Anglo-French blockade of the Río de la Plata formally declared.
- September 25 – The Phi Alpha Literary Society is founded.
- October 9 – The eminent and controversial Anglican, John Henry Newman, is received into the Roman Catholic Church.
- October 10 – In Annapolis, Maryland, the Naval School (later renamed the United States Naval Academy) opens with fifty midshipmen and seven professors.
- October 13 – A majority of voters in the Republic of Texas approve a proposed constitution, that if accepted by the United States Congress, will make Texas a U.S. state.
- October 21 – The New York Herald becomes the first newspaper to mention the game of baseball.
- October 22 – The New York Morning News becomes the first newspaper to include a box-score of a baseball game.
- November 20 – Anglo-French blockade of the Río de la Plata: Battle of Vuelta de Obligado: The Argentine Confederation is narrowly defeated by an Anglo–French fleet on the waters of the Paraná River but the victors suffer serious damage to their ships and Argentina attracts political support in South America.
- December 2 – Manifest destiny: U.S. President James K. Polk announces to Congress that the Monroe Doctrine should be strictly enforced and that the United States should aggressively expand into the West.
- December 11 – First Anglo-Sikh War: Sikh army crosses the Sutlej in the Punjab.
- December 5 – The Templars of Honor and Temperance is founded in the United States.
- December 22–23 – Battle of Ferozeshah (Anglo-Sikh War) – East India Company forces are victorious over those of the Sikh Empire.
- December 27 – Anesthesia is used for childbirth for the first time, by Dr. Crawford Long in Jefferson, Georgia.
- December 27 – American newspaper editor John L. O'Sullivan claims (in connection with the annexation of Texas) in The United States Magazine and Democratic Review that the United States should be allowed "the fullfillment of our manifest destiny to overspread the continent allotted by Providence for the free development of our yearly multiplying millions". It is the second time he uses the term manifest destiny and will have a huge influence on American imperialism in the following century.
- December 29 – Texas is admitted as the 28th U.S. state.
- December 30 – Queen's Colleges of Belfast, Cork, and Galway are incorporated in Ireland.
- The Republic of Yucatán separates for a second time from Mexico.
- Ephraim Bee reveals that the Emperor of China has given him a special dispensation: that he has entrusted him with certain sacred and mysterious rituals through Caleb Cushing, the U.S. Commissioner to China, to "extend the work and influence of the Ancient and Honorable Order of E Clampus Vitus" in the New World.
- Friedrich Engels' treatise The Condition of the Working Class in England is published in Leipzig as Die Lage der arbeitenden Klasse in England.
- Heinrich Hoffmann publishes a book (Lustige Geschichten und drollige Bilder) introducing his character Struwwelpeter, in Germany.
- The Ancient and Accepted Rite for England and Wales and its Districts and Chapters Overseas is founded[vague] in Freemasonry.
- Eugénie Luce founds the Luce Ben Aben School in Algiers.
- January 3 – Anna Edelheim, Finnish journalist (d. 1902)
- January 7
- February 2 – Ivan Puluj, Ukrainian physicist and inventor (d. 1918)
- February 14 – Quintin Hogg, British philanthropist (d. 1903)
- February 15 – Elihu Root, American statesman and diplomat, recipient of the Nobel Peace Prize (d. 1937)
- February 25 – George Reid, fourth Prime Minister of Australia (d. 1918)
- March 3 – Georg Cantor, German mathematician (d. 1918)
- March 4 – Henry Clay Taylor, American admiral (d. 1904)
- March 10 – Emperor Alexander III of Russia (d. 1894)
- March 20 – Victor Child Villiers, 7th Earl of Jersey, 18th Governor of New South Wales (d. 1915)
- March 27 – Wilhelm Röntgen, German physicist, Nobel Prize laureate (d. 1923)
- April 21 – William Healey Dall, American malacologist and explorer (d.1927)
- April 22 – Carlo Caneva, Italian general (d. 1922)
- April 24 – Carl Spitteler, Swiss writer, Nobel Prize laureate (d. 1924)
- May 4 – William Kingdon Clifford, English mathematician and philosopher (d. 1879)
- May 9 – Gustaf de Laval, Swedish engineer and inventor (d. 1913)
- May 12 – Gabriel Fauré, French composer (d. 1924)
- May 14 – Charles J. Train, American admiral (d. 1906)
- May 15 – Élie Metchnikoff, Russian microbiologist, recipient of the Nobel Prize in Physiology or Medicine (d. 1916)
- May 17 – Jacint Verdaguer, Catalan poet (d. 1902)
- May 25 – Eugène Grasset, Swiss-born artist (d. 1917)
- May 30 – King Amadeo I of Spain (d. 1890)
- June 7 – Leopold Auer, Hungarian violinist and composer (d. 1930)
- June 16 – Heinrich Dressel, German archaeologist (d. 1920)
- June 18 – Charles Louis Alphonse Laveran, French physician, recipient of the Nobel Prize in Physiology or Medicine (d. 1922)
- June 22 – Richard Seddon, 15th Prime Minister of New Zealand (d. 1906)
- July 4 – Thomas John Barnardo, Irish philanthropist (d. 1905)
- July 18 – Tristan Corbière, French poet (d. 1875)
- July 19 – Horatio Nelson Young, American naval hero (d. 1913)
- August 10 – Abai Qunanbaiuli, Kazakh poet (d. 1904)
- August 16
- August 19 – Edmond James de Rothschild, French philanthropist (d. 1934)
- August 21 – William Healey Dall, American naturalist, biologist and explorer (d. 1927)
- August 25 – King Ludwig II of Bavaria (d. 1886)
- September 1 – Paul Methuen, 3rd Baron Methuen, British field marshal (d. 1932)
- September 9 – Warner B. Bayley, United States Navy rear admiral (d. 1928)
- October 13 – Charles Stockton, American admiral (d. 1924)
- October 17 – John J. Gardner, American politician (d. 1921)
- October 21 – William McKendree Carleton, American poet (d. 1912)
- November 3 – Edward Douglass White, 9th Chief Justice of the United States (d. 1921)
- November 4 – Vasudev Balwant Phadke, Indian revolutionary (d. 1883)
- November 9 – Elizabeth Reed, subject of The Allman Brothers Band song "In Memory of Elizabeth Reed"
- November 10 – John Sparrow David Thompson, 4th Prime Minister of Canada (d. 1894)
- November 13 – Marta Abreu, Cuban philanthropist (d. 1909)
- December 9 – Joel Chandler Harris, American writer (d. 1908)
- January 11 – Etheldred Benett, British geologist (b. 1776)
- February 13 – Henrik Steffens, Norwegian philosopher (b. 1773)
- March – Nicolás Espinoza, Head of State of El Salvador (b. 1795)
- March 18 – Johnny Appleseed, American pioneer (b. 1774)
- March 19 – Seku Amadu, founder of the Fula Massina Empire (b. 1773)
- April 10 – Dr. Thomas Sewall, American anatomist (b. 1786)
- May 12
- May 15 – Braulio Carrillo Colina, Costa Rican Head of State (b. 1800)
- June 4 – Lasse-Maja, notorious Swedish criminal (b. 1785)
- June 8 – Andrew Jackson, 7th President of the United States (b. 1767)
- July 12
- July 17 – Charles Grey, 2nd Earl Grey, Prime Minister of the United Kingdom (b. 1764)
- August 23 – Rafael Urdaneta, hero of the Latin American War of Independence (b. 1788)
- October 12 – Elizabeth Fry, British humanitarian (b. 1780)
- October 26 – Lady Nairne, Scottish songwriter (b. 1766)
- Jones, Neal T., ed. (1984). A Book of Days for the Literary Year. New York; London: Thames and Hudson. ISBN 0-500-01332-2.
- Congress overrides presidential veto for first time. history.house.gov
- Penguin Pocket On This Day. Penguin Reference Library. 2006. ISBN 0-14-102715-0.
- "The Great Yarmouth Suspension Bridge Disaster – May 2nd 1845" (PDF). Broadland Memories. Archived from the original (PDF) on July 18, 2011. Retrieved 2010-10-14.
- The Hutchinson Factfinder. Helicon. 1999. p. 549. ISBN 1-85986-000-1.
- When the British decided they were going to bring Indians to Trinidad this year, most of the traditional British ship owners did not wish to be involved. The ship was originally named Cecrops, but upon delivery was renamed to Fath Al Razack. The ship left Calcutta on February 16.
- Fox, Stephen (2003). Transatlantic: Samuel Cunard, Isambard Brunel, and the Great Atlantic Steamships. HarperCollins. ISBN 978-0-06-019595-3.
- "Great Britain". The Ships List. Archived from the original on May 28, 2010. Retrieved 2010-10-01.
- Giraud, Victor (1890). Les lacs de l'Afrique Équatoriale : voyage d'exploration exécuté de 1883 à 1885 (in French). Paris: Librairie Hachette et Cie. p. 31.
- Palmer, Alan; Veronica (1992). The Chronology of British History. London: Century Ltd. pp. 267–268. ISBN 0-7126-5616-2.
- "Phytophthora infestans". A Short History of Ireland. BBC. Retrieved 2012-08-05.
- "E. Clampus Vitus". 2010. Retrieved 2010-10-01.
- "Luce Ben Aben School of Arab Embroidery I, Algiers, Algeria". World Digital Library. 1899. Retrieved 2013-09-26.