Fang: Hagrid's dog, a boarhound.
Fantastic Beasts and Where to Find Them: A first-year textbook. Also available in a Muggle edition.
Fat Friar: The house ghost of Hufflepuff.
Fat Lady: The painting that guards the Gryffindor dormitory.
Figg, Mrs. (PS ch. 2): A neighbor of the Dursleys who looks after Harry occasionally.
Etym: The name is properly derived from fig, but my guess is that if there is any meaning to it, Rowling is thinking more along the lines of the surname Figgis, from a nickname for a trustworthy or reliable person.
Filch, Argus: The caretaker of Hogwarts and terror of curfew-breakers.
Etym: Probably just the English word... thus, Argus Filch is on the lookout for all who might steal. (Doesn't do a very good job of it, does he?)
Finch-Fletchley, Justin (PS ch. 7): A Hufflepuff, the same year as Harry.
Etym: Finch means what it looks like, and I've no idea about the other part.
Finnigan, Seamus (PS ch. 7): A Gryffindor, the same year as Harry. His mother was a witch, and didn't tell his Muggle father until after they were married.
Etym: From the Gaelic name Fionn, meaning "white".
Firenze: A centaur who lives in the Forbidden Forest.
Etym: The modern Italian name for Florence.
Flamel, Nicholas (PS ch. 6): A 665-year-old alchemist and opera lover, a friend of Dumbledore's, and the creator of the only Philosopher's Stone known to be in existence.
Etym: The name of an actual historical alchemist. The Spell Binder has a lengthy article on him.
Flamel, Perenelle (PS ch. 13): Nicholas Flamel's wife, a mere 658 years old.
Flint, Marcus (PS ch. 11): A Slytherin, five years ahead of Harry. Chaser and captain of the Slytherin Quidditch team during Harry's first year.
Etym: Name for someone who lived near a notable outcrop of flint, or nickname for a hard-hearted individual.
Flitwick: The Charms teacher at Hogwarts.
Etym: A town in Bedfordshire; no etymology found, though.
Flourish and Blotts: A bookstore in Diagon Alley, the place where Hogwarts students buy their textbooks.
Etym: A flourish, in penmanship, is an added decoration. To blot is to dry wet ink by pressing something absorbent (like a blotting-paper) onto it, to absorb the excess and keep it from smudging. When writing with a fountain pen or quill, one would sign with a flourish and then blot it.
Fluffy: A cerberid dog acquired by Hagrid and put to work guarding the Philosopher's Stone.
Forbidden Forest: The woods adjoining Hogwarts, home to all sorts of magical creatures, including centaurs and possibly a werewolf or two.
Forgetfulness Potion: The final exam for Harry's first year of Potions.
Fred Weasley [Frederick]:
Etym: From Old German frithu "peace" + ric "ruler". The name of lots and lots of German kings.
From Egg to Inferno: Another of Hagrid's collection of books on dragon-rearing.
Fudge, Cornelius: The current Minister of Magic, although apparently unable to handle the job without constant advice from Dumbledore. If political events in the books match actual history, Fudge is a Tory (in fact, he bears a suspicious resemblance to one particular Tory) who is due to be replaced sometime in book 6 or 7 when Labour takes over the government.
Etym: Of all the meanings available, I think we should look at "false" or "clumsily forged".