Fag
The term fag derives from the word "flag" (as in: "His strength was flagging."). "Flag" appeared in the 16th century and was apparently a variant of the Middle English word flacken. Flacken meant "to flutter", and was influenced by the Old French word flaquir. Flaquir meant "to be flaccid." The word "fag" came to mean "thing hanging loosely," and was applied to the remnants of a bolt of cloth, the tail end of an originally long spool of rope, etc., It therefore had the derived meaning of any off-cut or unwanted part of any product, such as wood, cloth or meat, known as a "fag-end." The associations among the various strands of meaning of "fag," such as "to flutter," "to be flaccid," "thing hanging loosely," "the last and worst part of anything" seem to be better connected to the pejorative present-day sense of "faggot" and "fag" than are the dictionary meanings of the word "faggot," which were limited strictly to the sense of "bundle" before the middle of the 20th century.
In British English, the word "fag" was used (as a verb and a noun) to refer to a kind of apprenticeship practiced within public schools. Younger boys within the school "fagged" for the older boys by cooking breakfasts, cleaning sports kit or other menial tasks. The term fag in this sense derived from the sense "flagging in energy due to having performed strenuous menial labour," as in "I'm all fagged out." Violence, bullying and sexual abuse were sometimes associated with fagging. As public schools have become more exposed to public scrutiny, fear of litigation has caused the practice of fagging to be banned in most schools.
In modern British English, "fag" is a colloquialism for a cigarette, as in "I'm gasping for a fag", "Where can I get some fags?", or "Can I bum a fag?" (can I borrow a cigarette?). It was originally a reference to a cigarette-butt or cigar-butt and comes from the expression "fag-end," meaning the leftover or useless part of any thing.
In American English, "fag" is used as an abbreviated form of "faggot", a pejorative term for gay men. This meaning has also become understood as an Americanism in British English, primarily due to the use of it on film and television series imported from the United States.