"Can I say poo?"
This is often how I would start a beginning design class, during the second week of school. Of course, I wanted it to sound silly and to get a Yes or a nod from most in the class. Then on to 'crap' and 'shit'.
The class goes along. Then, how about the word 'fuck'? Can I say that. A bit quieter, a few awkward giggles, but no objections.
This leads us to a discussion about words and their power. Words do have power, but its not inherent in the letter symbols - its what our perceptions and attitudes have embellished the word with. The letters f u c k are just that - a group of letter symbols. Like in the initials French Connection United Kingdom:

Graphic designers primarily work with letter symbols and their words to clearly communicate a message. Words do have power.

Once 'dirty' words become more common and more widely used, their power to offend will be removed. It will be a great day when there are no more offensive words. No more gasps, slaps, insults, slurs, outrage, discomfort, or complaints.

"Words are innocent, its the intention behind the words you ought to be concerned about" - George Carlin

Wisdom from the comedian Lenny Bruce
"Are there any niggers here tonight?" Now what did he say? "Are there any niggers here tonight?" I know there's one nigger, because I see him back there working. Let's see, there's two niggers. And between those two niggers sits a kyke. And there's another kyke - that's two kykes and three niggers. And there's a spic. Right? Hmm? There's another spic. There's a wop; a polack; and, oh, a couple of greaseballs. And Irish micks.
Well, I was just trying to make a point, and that is this: it's the suppression of the word that gives it the power, the violence, the viciousness. Dig: if President Kennedy would just go on television, and say, "I would like to introduce you to all the niggers in my cabinet," and if he'd just say "nigger nigger nigger nigger nigger" to every nigger he saw, "boogie boogie boogie boogie boogie," "nigger nigger nigger nigger nigger" 'til nigger didn't mean anything anymore, then you could never make some six-year-old black kid cry because somebody called him a nigger at school.
- From Lenny Bruce: Swear to tell the truth

The origin
Rumors persist that acronyms spawned the obscenity: "Fornication Under Consent of the King" or the Irish police inscription "booked For Unlawful Carnal Knowledge". But, the modern-day word was first printed in a Scottish poem in 1503 and has been traced to a number of etymological origins: Middle Dutch (fokken), Germanic (ficken), English (firk), Scottish (fukkit). Even the Latin term futuerre (to copulate) bears a resemblance to the four-letter word. Of course, its original definition linking sex with violence and pleasure with pain has broadened considerably in the past 500 years.
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However, people may have used the word in 1310. When British Historian Paul Booth of Keele University was flipping through a court document from the city of Chester, he made an entirely unexpected discovery: An outlaw listed by the name of "Roger Fuckebythenavele" appears three times in the document, suggesting that "Fuckebythenavele" was a nickname and not simply a one-time joke. This marks the oldest written use of the f-word in the English language.

Besides the sexual connotations, the word fuck can be used to describe many types of situations
    Aggression: Don't fuck with me buddy.
    Amazement: Well, fuck.
    Anger: Fuck it.
    Confusion: What the fuck is going on?
    Curiosity: What the fuck are you doing?
    Despair: Fucked again.
    Difficulty: I don't understand the fucking question.
    Dissatisfaction: I don't like what the fuck is going on here.
    Dismay: ahhh fuck it.
    Displeasure: What the fuck is happening?
    Enhance the meaning of a word: Beautifuckingful or infuckingcredible.
    Fear: Oh fuck.
    Fraud: I got fucked at the used car lot.
    Frustration: Fuck.
    Incompetence: He's all fucked up.
    Inquiry: Who the fuck was that?
    Laziness: He's just fucking around.
    Rebellion: Fuck off.
    Self-confidence: I don't give a fuck.
    Trouble: I guess I'm really fucked now.
    Uncaring: Who gives a fuck?

Examples of the word in use

A few examples from New York magazine, 2010:

Above: Promos for the play. Below: Promo in 'uptight' Oklahoma City.

Some instances when saying fuck is appropriate