Famous birthdays, deaths and events of 1720
- January 4 - Johann Friedrich Agricola, German composer (d. 1774)
- February 26 - Gian Francesco Albani, Italian Catholic cardinal (d. 1803)
- March 13 - Charles Bonnet, Swiss naturalist and writer (d. 1793)
- April 23 - Vilna Gaon, Lithuanian rabbi (d. 1797)
- August 12 - Konrad Ekhof, German actor (d. 1778)
- August 18 - Laurence Shirley, 4th Earl Ferrers
- October 3 - Johann Peter Uz, German poet (d. 1796)
- October 19 - John Woolman, American Quaker preacher and abolitionist (d. 1772)
- November 16 - Carlo Antonio Campioni, Italian composer (d. 1788)
- April 21 - Antoine Hamilton, French writer (b. 1646)
- June 27 - Guillaume Amfrye de Chaulieu, French poet (b. 1639)
- August 9 - Simon Ockley, English orientalist (b. 1678)
- November 17 - Calico Jack, English pirate (b. 1682)
- January 6 - The Committee of Inquiry on the South Sea Bubble publishes its findings.
- January 21 - Sweden and Prussia sign the Treaty of Stockholm.
- February 29 - Queen Ulrika Eleonora of Sweden abdicates in favour of her husband, who becomes King Frederick I.
- July 27 - The second important victory of the Russian Navy