My favorite puzzles have already been posted (blue eyes, 100 prisoners), so I'll just post a somewhat easy one:
7 pirates have just ended plundering the Caribbean, so they get together to discuss how they will share the 100 gold coin booty. Now, these aren't your normal kind of pirates, they are blood-thirsty, unlimitedly greedy, perfectly rational pirates, and they are ranked by fighting prowess.
Thus, the captain has to propose how to share the booty, knowing that if more than half of his crew starts a mutiny, he will get killed, and the 2nd in command will take his place (who will in turn have to propose how to share the booty, eventually being replaced by the third in command, etc.).
How much gold will each pirate receive?