This is an old word. OLD. In fact, we aren't entirely certain we can trace it back definitively because it was so much more prevalent in common speech than in written form. It is assumed to originate from the germanic languages (the German "f****n", the Dutch "fokken", the Norwegian "f*kka" and the Swedish "fokka") but there are similar usages in the Latin/Greek languages. For example: the Latin "f*tere", the French "foutre", the Italian "fotre", and so on. The latin origination theory, however, would have to explain how the word reached Scandinavia via Roman contact and how the 't' sound became a 'k' sound.

There are plenty of urban legends surrounding the history of this particular word, but most have been found to be false. For example, the word "f**k" did not come from "File Under Carnal Knowledge", "Fornication Under the Command of the King", False Use of Carnal Knowledge", and any other iterations involving acronymns.

The first known occurrence of the word (at least the most accepted) is in code in a poem in a French/Latin mix which satirizes the Carmelite monks of Cambridge from around 1500. The line reads "They are not in heaven because they f**k wives of Ely". It was probably coded because it spoke poorly of clergy... not something that would usually get into print since so much of the written word of that day was written BY clergy.