In the Philippines, it was the only leap year with 365 days, as December 31 was skipped when 1845 began after December 30. The change also applied to Caroline Islands, Guam, Marianas Islands, Marshall Islands, and Palau as part of the Captaincy General of the Philippines. And became the first places on Earth to redraw the International Date Line.
January 15 – The University of Notre Dame, based in the city of the same name, receives its charter from Indiana.
February 27 – The Dominican Republic gains independence from Haiti.
February 28 – A gun on the USS Princeton explodes while the boat is on a Potomac River cruise, killing two United States Cabinet members and several others.
March 8
King Oscar I ascends to the throne of Sweden–Norway upon the death of his father, Charles XIV/III John.
The Althing, the parliament of Iceland, is reopened after 45 years of closure.
March 9 – Giuseppe Verdi's opera Ernani debuts at Teatro La Fenice, Venice.
March 12 – The Columbus and Xenia Railroad, the first railroad planned to be built in Ohio, is chartered.
March 13 – The dictator Carlos Antonio López becomes first President of Paraguay.
March 21 – The Baháʼí calendar begins.
March 23 – The Edict of Toleration is passed in the Ottoman Empire.
May 1 – The Hong Kong Police Force, the world's second and Asia's first modern, police force is established.
May 23 – Persian prophet The Báb privately announces his revelation to Mullá Husayn, just after sunset, founding the Bábí faith (later evolving into the Baháʼí Faith as the Báb intended) in Shiraz, Persia (modern-day Iran). Contemporaneously, on this day in nearby Tehran, is the birth of Abdu'l-Bahá; the eldest Son of Bahá'u'lláh, Prophet-Founder of the Baháʼí Faith. The Báb's mission is to proclaim He whom God shall make manifest.
Abdu'l-Bahá Himself is later proclaimed by Bahá'u'lláh to be His own successor, thus being the third "central figure" of the Baháʼí Faith.
May 24 – The first electrical telegram is sent by Samuel Morse from the U.S. Capitol in Washington, D.C.