Compasses have been used by a number of characters in Lost, most often for navigation. They are necessary for getting to and from the Island on the correct bearing; however, they do not appear to function correctly onthe Island.
On the Island
Richard Alpert gave Locke his compass, instructing him to give it back to him the next time Locke saw him. ("Because You Left") When Locke time-shifted to 1954, he gave the compass to Richard in order to prove he was from the future. ("Jughead") In 2007, The Man in Black posing as Locke told Richard to give the compass to Locke, thereby creating a time loop. ("Follow the Leader") It is also something of a self-contained paradox, since the compass was never created.