1668 (MDCLXVIII) was a leap year starting on Sunday of the Gregorian calendar and a leap year starting on Wednesday of the Julian calendar, the 1668th year of the Common Era (CE) and Anno Domini (AD) designations, the 668th year of the 2nd millennium, the 68th year of the 17th century, and the 9th year of the 1660s decade. As of the start of 1668, the Gregorian calendar was 10 days ahead of the Julian calendar, which remained in localized use until 1923.
|Ab urbe condita||2421|
|Balinese saka calendar||1589–1590|
|English Regnal year||19 Cha. 2 – 20 Cha. 2|
|Chinese calendar||丁未年 (Fire Goat)|
4364 or 4304
— to —
戊申年 (Earth Monkey)
4365 or 4305
|- Vikram Samvat||1724–1725|
|- Shaka Samvat||1589–1590|
|- Kali Yuga||4768–4769|
|Japanese calendar||Kanbun 7|
|Julian calendar||Gregorian minus 10 days|
|Minguo calendar||244 before ROC|
|Thai solar calendar||2210–2211|
1794 or 1413 or 641
— to —
1795 or 1414 or 642
- January – The Triple Alliance of 1668 is formed between England, Sweden and the United Provinces.
- February 13 – In Lisbon, a peace treaty is established between Afonso VI of Portugal and Carlos II of Spain, by mediation of Charles II of England, in which the legitimacy of the Portuguese monarch is recognized. Portugal yields Ceuta to Spain.
- May 2 – The first Treaty of Aix-la-Chapelle ends the War of Devolution.
- July 7 – Bishop Isaac Barrow founds the Bishop Barrow Trust with the intention of establishing a university on the Isle of Man; this becomes King William's College.
- July – Welsh privateer Henry Morgan sacks Portobello and Panama City; the lack of booty from the latter attack leads to the city being burned.
- September 9 – Molière's comedy The Miser (L'Avare) is first performed, in Paris.
- September 21 – The British East India Company takes over Bombay under a Royal Charter of March 27.
- One of the world's earliest central banks, the Sveriges Riksbank, is founded in Stockholm, Sweden.
- Emperor Yohannes I of Ethiopia convenes a church council in Gondar, which decides to expel all Roman Catholics from the country.
- English scientist Isaac Newton builds the first reflecting telescope (Newton's reflector).
- May 8 – Alain-René Lesage, French writer (d. 1747)
- June 23 – Giambattista Vico, Italian philosopher and historian (d. 1744)
- July 21 – Frederick Heinrich of Saxe-Zeitz-Pegau-Neustadt (d. 1713)
- September 8 – Giorgio Baglivi, Armenian doctor and writer (d. 1707)
- October 18 – John George IV, Elector of Saxony (d. 1694)
- October 30 – Sophia Charlotte of Hanover, sister of King George I of Great Britain (d. 1705)
- November 10
- November 11 – Johann Albert Fabricius, German scholar (d. 1736)
- November 27 – Henri François d'Aguesseau, Chancellor of France (d. 1751)
- November 30 – William August, Duke of Saxe-Eisenach (d. 1671)
- December 11 – Apostolo Zeno, Italian poet and journalist (d. 1750)
- December 31 – Herman Boerhaave, Dutch humanist and physician (d. 1738)
- date unknown – Stokkseyrar-Dísa, Icelandic Galdrmistress (d. 1728)
- January 6
- January 14 – Arnauld de Oihenart, Basque historian and poet (b. 1592)
- January 31 – Hermann Busenbaum, German Jesuit theologian (b. 1600)
- February 2 – Antonio del Castillo y Saavedra, Spanish artist (b. 1616)
- February 8 – Alessandro Tiarini, Italian painter (b. 1577)
- February 21 – John Thurloe, English Puritan spy (b. 1616)
- March 16 – Francis Talbot, 11th Earl of Shrewsbury (b. 1623)
- April 12 – Alexander Daniell, sole proprietor of the Manor of Alverton, Cornwall (b. 1599)
- April 21 – Jan Boeckhorst, Flemish painter (b. c. 1604)
- May 1 – Frans Luycx, Flemish painter (b. 1604)
- May 8 – Catherine of St. Augustine, French nun and nurse of New France (b. 1632)
- May 9 – Otto Christoph von Sparr, German general (b. 1599)
- May 21 – Christoph Delphicus zu Dohna, Prussian-born Swedish soldier, diplomat (b. 1628)
- June 20 – Heinrich Roth, German Sanskrit scholar (b. 1620)
- July 26 – Hans Svane, Danish statesman (b. 1606)
- August 9 – Jakob Balde, German Latinist (b. 1604)
- August 23 – Artus Quellinus the Elder, Flemish sculptor (b. 1609)
- August 24 – Tyman Oosdorp, Dutch brewer and magistrate of Haarlem (b. 1613)
- September 16
- September 19 – Sir William Waller, English Civil War general (b. c. 1635)
- October 12 – Zacharias Wagenaer, secretary, painter, then merchant and administrator (Dutch East-India Company) (b. 1614)
- October 13
- November 17 – Joseph Alleine, English non-conformist preacher (b. 1634)
- November 21 – Adolf William, Duke of Saxe-Eisenach (b. 1632)
- December 3 – William Cecil, 2nd Earl of Salisbury, English earl (b. 1591)
- December 14 – Charles Berkeley, 2nd Viscount Fitzhardinge, English politician (b. 1599)
- December 23 – Martin Bauzer, Gorizian Jesuit priest and writer (b. 1595)
- December 24 – Wadham Wyndham, English judge (b. 1609)
- unknown date – Fang Weiyi, Chinese poet, calligrapher, painter and literature historian (b. 1585)
- "Bishop Barrow's Historic Deed". Journal of the Manx Museum. Retrieved August 28, 2014.
- Hall, Rupert (April 11, 1996). Isaac Newton: adventurer in thought. p. 67. ISBN 9780521566698.
- Almut Spalding; Almut Marianne Grützner Spalding (2005). Elise Reimarus (1735-1805). Königshausen & Neumann. p. 518. ISBN 978-3-8260-2813-7.
- Gerrit Arie Lindeboom (1968). Herman Boerhaave: The Man and His Work. Methuen. p. 4. ISBN 978-0-416-10880-4.
- Rudolf Steiner (1975). Between Death and Rebirth: Ten Lectures Given in Berlin Between 5th November, 1912 and 1st April, 1913. Rudolf Steiner Press. p. 69. ISBN 978-0-85440-287-8.
- Programm und Jahresbericht des K.K. Ober-Gymnasiums in Görz am Schlusse des Schuljahres 1856 (in German). J. B. Seitz. 1856. p. 7.
- Kang-i Sun Chang; Haun Saussy; Charles Yim-tze Kwong (1999). Women Writers of Traditional China: An Anthology of Poetry and Criticism. Stanford University Press. p. 284. ISBN 978-0-8047-3231-4.