January 1 – The British Empire (except Scotland, which had changed New Year's Day to 1 January in 1600) adopts today as the first day of the year as part of adoption of the Gregorian calendar, which is completed in September: today is the first day of the New Year under the terms of last year's Calendar Act of the British Parliament.
April 6 – Spanish Governor Tomás Vélez Cachupín of Santa Fe de Nuevo México, a province that now comprises most of the American state of New Mexico, begins the first peace negotiations with the indigenous Comanche tribe after inviting tribal representatives to his home in Taos. As a sign of good faith, he unconditionally releases the four Comanche prisoners of war held at Taos. One of the released Comanches reports to his father, Chief Guanacante, about the hospitality extended to him during his imprisonment, and more meetings take place in July and in the autumn.
April 13 – The oldest property insurance company in the United States, "Philadelphia Contributionship for the Insurance of Houses from Loss by Fire", holds its organizational meeting at the courthouse in Philadelphia to elect a board of directors, largely through the efforts of Benjamin Franklin. Franklin's newspaper, The Pennsylvania Gazette, has been advertising the meeting since February 18, with a notice that "All persons inclined to subscribe to the articles of insurance of houses from fire, in or near this city, are desired to appear at the Court-house, where attendance will be given, to take in their subscriptions, every seventh day of the week, in the afternoon, until the 13th of April next, being the day appointed by the said articles for electing twelve directors and a treasurer."  The property insurance company is still in existence more than 250 years later.
April 22 – Adam Smith, appointed the year before as a professor of logic, is unanimously elected by the faculty of the University of Glasgow to be the new Professor of Moral Philosophy "on the express condition that he would content himself with the emoluments of the Logic Professorship until 10 October", in that the 1751-1752 salary budgeted for the job has already been distributed to faculty members who had substituted for the previous moral philosophy professor, Thomas Craigie; from April to October, Smith's remuneration for teaching moral philosophy is limited to fees paid directly to him by his students (a half guinea per semester for the public class, and a guinea per semester for the private class. Smith's lectures on ethics are first published in 1759 in his work The Theory of Moral Sentiments.
June – Benjamin Franklin reportedly carries out his famous kite experiment, duplicating experiments that show that lightning and electricity are the same. According to Franklin, lightning strikes the kite that he is flying during a thunderstorm and produces sparks identical to what he has previously generated artificially in a Leyden jar. However, the report of his experiment is not made until October 19, in Franklin's newspaper, The Pennsylvania Gazette, leading 20th century researchers to doubt that he conducted the experiment, if at all, until sometime after September 28, when he had written in the Gazette about other such experiments, and that he was making a claim that he had conceived the experiment independently.
June 3 – A fire destroys 13,000 houses in Moscow, capital of the Russian Empire, only 11 days after a May 23 fire destroyed 5,000 homes; by June 6, two-thirds of the city has been damaged or destroyed .
July 30 – The first of the Kronstadt canals, conceived by Peter the Great and designed to link two of the harbors of the Russian city, is completed and opened to maritime traffic.
August 3 – Edward Cornwallis, the British Governor of Nova Scotia, is recalled to Britain after being unsuccessful in pressuring Nova Scotia's Acadian population to take an oath of allegiance to the Crown or to face expulsion. His replacement, Peregrine Hopson, is more lenient with the Acadians but is reassigned less than two years later.
August 25 – The first group of the United Brethren church, commonly called the Moravians, leaves Bethlehem, Pennsylvania on a mission to find 100,000 acres (40,000 ha) of land on which to build "Villages of the Lord" for German emigres to settle upon in America; after a 450 miles (720 km) journey, they arrive in Edenton, North Carolina on September 10 and eventually purchase the
Wachovia tract, a set of lands in the western North Carolina colony.
September 2 of Julian calendar (Wednesday) (September 13 "New Style") – Great Britain and the British Empire use the Julian calendar for the last time and adopt the Gregorian calendar, making the next day Thursday, September 14 in the English-speaking world. A newspaper at the time notes the next day that "Altho' we have more than once, for the Information of our Readers, publish'd some Accounts of the Alteration of the Style, which took Place this Day, agreeable to a late Act of Parliament, in all his Majesty's Dominions in Europe, Asia, Africa and America" and notes that "The Supputation of the Year began on the first Day of January last, and for the future the first Day of that Month will be stiled the first Day of every Year in all Accounts whatsoever, which Supputation or Reckoning never took Place before this Year in any Courts of Law until the 25th Day of March", and adds, "This Day, had not this Act passed, would have been the 3rd of September, but is now reckoned the 14th, eleven nominal Days being omitted." 
October 19 — In his Philadelphia newspaper, the Pennsylvania Gazette, Benjamin Franklin first describes the performance, in Philadelphia of the kite experiment that he had proposed in his 1750 book. Although the original account makes no claim that he was the first to do the experiment (which had been done by other scientists (including Thomas-François Dalibard in May), nor that he conducted the test, and it does not give a date for the experiment, it becomes embellished as the story that Franklin "discovered electricity"; in 1766, the story first circulates that Franklin flew the kite in June, 1752, without specifying a date (as Franklin had done in other scientific accounts). 
November 3 – A hurricane destroys the Spanish settlement on Florida's Santa Rosa Island, leaving only two buildings standing; the remaining residents decide to move from the barrier island on the Gulf of Mexico and to start a settlement on the nearby mainland and construct the Presidio San Miguel de Panzacola, which later forms the nucleus of the city of Pensacola, Florida.