Twenty (vingt) is used as a base number in French. E.g. quatre-vingt means 4 times 20, i.e. 80.
Twenty (tyve) is used as a base number in the Danish language: Tres (short for tresindstyve) means 3 times 20, i.e. 60; firs (short for firsindstyve) means 4 times 20 i.e. 80. halvtreds means (3 - 1/2) times 20, i.e. 50; halvfjerds means (4 - 1/2) times 20, i.e. 70; and halvfems means (5 - 1/2) times 20, i.e. 90.
Twenty (ugain) is used as a base number in the Welsh language, although in the latter part of the twentieth century a decimal counting system came to be preferred, with the vigesimal system becoming 'traditional'. Deugain means 2 times 20 i.e. 40, trigain means 3 times 20 i.e. 60. Prior to the currency decimalisation in 1971, papur chwigain (6 times 20 paper) was the nickname for the 10 shilling (=120 pence) note.
Twenty may have been the base of the Maya number system, see Maya numerals and Maya calendar.
In the old British currency system, there were twenty shillings in a pound.
In English, counting by the score has been used historically, as in the famous opening of the Gettysburg Address "Four score and seven years ago...", meaning eighty-seven years ago. This usage has fallen into disuse in modern times, however.