I've always got a kick out of the quest story where the hero is given a series of impossible tasks to complete, and yet somehow manages them.
Sometimes the hero manages them through sheer bravery and force of will; other times, the tasks are met with the aid of friends. Most frequently, though, the impossible becomes not only feasible but fairly obvious in hindsight.
The Mabinogion relates a few of the first sort of quest, in the person of Pwll as he journeys into Annwn, though I especially remember a story where a hero is given 46 impossible tasks to accomplish before he may marry the woman he loves. He gets the help of King Arthur and the other knights, but only does three or four of them before the bard loses interest, and they go kill the giant and the knight marries his lady-love.
Perhaps a better example is the Russian fairy story about a prince who is pledged to be given to the Devil, but he is able to outsmart the Devil with the help of a beautiful woman who has learned magic, so that he is able to spot the true tsarina among a group of 46 women indentical in every way.
Or what about the wise woman from Chinese folklore who is told she must capture wind and fire upon and within paper, and so she invents the fan and the lantern? The emperor hears great boasts of her beauty, and so he commands her to tell him where the center of the world is, and she replies, "It is directly in front of you; if not, please tell me where it is, that I may be corrected." And when he orders hre to squeeze enough grapes to fill the ocean, she replies, "Certainly. First please tell me how large the ocean is, that I may begin filling it."
Or there's this song, made popular by Simon and Garfunkel, about a woman who sets before her unfaithful lover a series of impossible tasks to regain his place in her affections:
Amazon.com: Luvvies Ballerina Purple Hippo 5": Toys & Games (clipped to polyvore.com)