According to the Chambers Dictionary of the Unexplained, April Fool's Day may have originated with the introduction of the Gregorian calendar. Those who had gone along with the change—celebrating New Year's on the first of January—"began to make fun of those who persisted in celebrating New Year's Day on 1 April because they either had not yet heard of the change or stubbornly refused to adopt it...over time this evolved into a general tradition of playing tricks on people and sending them on fool's errands on 1 April."
The entry also offers a few traditional dos and don'ts. "Any joke or trick must be played before noon; after that, it is said to rebound on the trickster. Anyone who takes an April Fool's Day joke in bad part is thought to risk bad luck, while a more optimistic belief holds that if a trick is played on a man by a pretty girl, he will be compensated later by her marrying him. Getting married on 1 April is not recommended for men, however, because it is believed that a man who marries on this date will be ruled by his wife from that day on. It is also said that children born on April Fool's Day will enjoy good luck in most respects, but will be disastrously unlucky gamblers."
Lastly, the entry mentions a BBC documentary on the "Swiss Spaghetti Harvest" that aired on April 1, 1957. In a black-and-white photo, a girl plucks strings of spaghetti that are hanging from a tree. She is admirably stone-faced. (Click here for the original clip on Youtube. Spaghetti weevil! Bwahahaha!)