late Old English curs "a prayer that evil or harm befall one; consignment of a person to an evil fate," of uncertain origin. No similar word exists in Germanic, Romance, or Celtic. Middle English Dictionary says probably from Latin cursus "course" (see course (n.)) in the Christian sense "set of daily liturgical prayers" extended to "set of imprecations" as in the sentence of the great curse, "the formula read in churches four times a year, setting forth the various offenses which entailed automatic excommunication of the offender; also, the excommunication so imposed." Connection with cross is unlikely. Another suggested source is Old French curuz "anger."
Meaning "the evil which has been invoked upon one, that which causes severe trouble" is from early 14c. Curses as a histrionic exclamation ("curses upon him/her/it") is by 1680s. The curse in 19c. was the sentence imposed upon Adam and Eve in Genesis iii.16-19. The slang sense "menstruation" is from 1930. Curse of Scotland, the 9 of diamonds in cards, is attested from 1791, but the signification is obscure.