Actually, it's commonly (although incorrectly) assumed that 'Fuck' is an acronym meaning either "Fornication Under Consent of the King" or "For Unlawful Carnal Knowledge." These are not the case.
Tracing the history of the word 'Fuck' has proven difficult over the years, as it has been a taboo for most of its existance. Citations are also quite rare. According to "American Heritage", the earliest known use predates the year 1500. It is used in a poem written in both English and Latin called "Flen flyys."
"Non sunt in celi quia fuccant uuiuys of heli."
Translates to:
"They (the monks) are not in heaven because they fuck the wives of Ely (a town near Cambridge)."
(Fuccant is a pseudo-Latin word.)
The earliest citation of its current spelling is from 1535.
The root of the word is almost definitely Germanic. Proof of this lies in the fact that it has cognates in other Northern European languages - for example, Middle Dutch fokken meaning to thrust, to copulate with; dialectical Norwegian fukka meaning to copulate; and dialectical Swedish focka meaning to strike, push, and copulate, as well as fock meaning penis. French has the word foutre, while Italian has fottere - both of which are derived from the Latin word futuere.