- There is a general election. In Co. Tipperary, Sir Thomas Maude declares himself a candidate and threatens to petition against another candidate, Thomas Mathew, on the grounds that Mathew is Catholic in all but name. Daniel Gahan, agent for Maude, subsequently kills Thomas Prendergast, Mathew’s agent, in a duel. Mathew is elected but is declared not duly elected after a petition from Maude, who thus gains the seat
- In the climate of sectarian tension created partly by the Mathew–Maude controversy, the Whiteboys, a violent agrarian protest movement, begins in Tipperary and spreads through Munster and West Leinster (October–December).
- John MacNaghten, a gambler, duellist and criminal born in Ballymoney, Co. Antrim, who had been involved in the killing of Mary Anne Knox, daughter of Andrew Knox MP, is hanged for murder at Strabane jail on 15 December. At the first attempt to hang him the rope breaks but, eschewing offers from the crowd to help him make his escape, he declares that he does not wish to be known for ever as ‘half-hung McNaghten’ and asks the hangman to proceed. (He is nevertheless known as ‘half-hung McNaghten’.)
- Richard Nugent (Lord Delvin), MP for Fore and still a teenager, fights a duel with a Mr Reilly on 30 July and dies of his wounds on 6 August. Duelling will reach a peak in Ireland in the 1770s and 1780s.
- Those born in Ireland in 1761 include two giants: Charles Byrne, who will be eight feet tall at 19 years of age, and Patrick Cotter (born in Kinsale, Co. Cork), who will be 97 inches tall according to his coffin plate. Other births include political radicals such as Edward Hay, James Coigley and the deportee Samuel Neilson. Dorothy Jordan, a famous Drury Lane actress and the mother of ten children by the future William IV, is born near Waterford.