Begging the Question

Also called "Petitio principii", this is "proving" that something is true by taking your conclusion as one of your premises, usually done implicitly rather than explicitly. Few people are fooled by having your conclusion as your only premise, as in "Joe is mad at Jill, therefore Joe is mad at Jill.". Such arguments are called tautologies and are valid, and sound if the premises are true, but utterly meaningless. Put broadly, this fallacy applies to any argument where one or more premises are at least as contentious as the conclusion itself, and for the same reasons, such as:

"Alice says she is honest. If an honest person says something, it must be true. Therefore Alice is an honest person, because an honest person says so."

"Begging the question" has come to mean "leading inevitably to the question" in the popular media, though this usage is a common Berserk Button for academics aware of the original use noted above. Nevertheless, to avoid confusion, this fallacy is sometimes referred to by its Latin name, petitio principii in more formal settings.

See also No True Scotsman.

Comics

 * A classic Bill Mauldin political cartoon from the early 1960s features an American soldier standing in a field of large cartoon mushrooms, a shout-out to the conical hats worn by Asian field workers and guerrillas, explaining to a comrade the challenge of ground combat in Vietnam: "You got your mushrooms and your toadstools. The mushrooms are harmless, the toadstools will kill you. You'll know it's a toadstool if it kills you."
 * Most -- if not all -- of Jack Chick's characters use this as an underlying point of their argument. Christianity is the one true religion (and thus the only way to save yourself) because the Bible says so, and we know we can trust the bible because it's the book of the one true religion.

Video Games

 * Similar to the "mushrooms" example above, in Metal Gear Solid 3: Snake Eater, Snake wants to know the difference between two snakes who look very similar, but one of which will poison him if he eats them. Para-Medic suggests an easy way to tell them apart: eat one. If it's poisonous, then he knows it's the poisonous one.

Web Comics
"Reynardine: Your powers of trickery and deception are bewildering, child."
 * Antimony uses almost this exact argument in this Gunnerkrigg Court strip.
 * Of course, it's rather justified, as it's against robots who have trouble understanding this fallacy.

Web Original

 * In the days of Usenet, in a football forum, one poster postulated that you need a great coach to win a Super Bowl. He then defined a "great coach" as one who had won a Super Bowl.

Real Life

 * A common question asked of atheists by theists is "If God didn't create the universe, who did?" The phrase 'who did' means that the question already assumes the universe was created by some intelligent entity. Strictly speaking, asking "Then where did the universe come from" also assumes that the universe was not eternal. In cases such as these, the question begging is generally accidental and more a problem resulting from conventional speech.
 * IIRC, the steady state theory of cosmology is pretty much deprecated by now, so asking 'where did the universe come from if it wasn't here all along?' is a valid scientific question again.