The first witch that most Italian kids hear about, and the one they annually await most expectantly, is Befana, the gift-giving good witch who visits Italian homes on the Feast of the Epiphany, January 6. Epiphany is the traditional commemoration of the arrival of the Magi with gifts for the twelve-day-old Jesus in Bethlehem.
According to the most prevalent Befana story, the Magi asked an old woman in Bethlehem to help them find the baby Jesus, but she was too busy sweeping out her house and sent them on their way unassisted. Within minutes, the old woman repented her unkindness and ran out to help in the search for Jesus, but the Magi were by then out of site. She searched for them, broom in hand, but never quite caught up. To this day the old lady searches, particularly on the feast of the Epiphany. She brings along plenty of gifts for Jesus, but willingly parts with some of them when she finds other children.
Befana, in some versions of the story, runs so fast seeking Jesus that she eventually takes off and flies, using her broom for steering. Over the centuries, Befana came to be identified as a witch, probably because of other, less savory old ladies flying in the area with brooms. Nobody knows the real name of the Befana -- according to many Befana theorists, Befana is merely a corruption of the name of the Epiphany feast on which she is most active.
Somewhere along the line, Befana acquires a western sense of justice and begins to give gifts only to good children -- bad kids get lumps of coal. But all kids, with irrepressible optimism, hang up their stockings or put their shoes near the door for Befana to fill on the night before Epiphany. And their optimism is well founded: Befana is really too kind, so even bad kids don't get real coal. Instead, there are lumps of black sugar candy that look like coal -- every stocking probably deserves at least one such reminder that, hard as he or she may try to be good, no kid is perfect. Hang a Befana doll or maybe just a small broom on your door to let her know she's welcome.
Befana, of course, is not the only person who gives gifts. Parents, friends, relatives, everyone thinks Befana's kindness should be emulated, so gifts are exchanged all around on the feast of the Epiphany. But what about Christmas presents? In recent years, Babbo Natale, a clone of the American Santa Claus, has started to show up in some houses on Christmas morning with his own bag of goodies. Nobody objects, but he shouldn't replace Befana -- she should come as scheduled, twelve days later. And nobody tries to prevent Saint Nicholas leaving presents on his feast day, December 6 -- he comes mostly on the Adriatic coast in the Bari area, where he is specially venerated, and in the Tyrol, where northern customs have crept in. In Sicily, Santa Lucia comes with gifts on the night before her feast, December 13th. Some Romans still follow the ancient Saturnalia/New Year gift-giving tradition, although, because of calendar reforms, the date has shifted from the solstice to December 31. Kids all over Italy encourage such proliferation.
Other Befana lore is at http://fabrisia.com/befana.htm and at http://www.voicenet.com/~mimir/Befana.html .
More comprehensive Italian Christmas tradition sites are at http://www.towerofbabel.com/sections/ourmaninhavana/ourwomaninitaly/marialamkin/natale/english/.
P.S.: Did you know that the popular Mexican/Spanish/US Christmas and party tradition of striking candy-filled piñatas entered Europe through Italy? Piñata scholars say Marco Polo saw similar Chinese-New-Year happenings and brought the idea home to Venice in the 13th century. The etymology of the Italian word Îpignattaâ is obscure -- it now means a thin and therefore fragile clay cooking pot, but it may originally have referred to a purposely weakened or scored clay vessel designed to be broken in the piñata/pignatta game: the scored pot inside the decorations would look like the familiar pigna pine cone. Read about it at http://www.mexconnect.com/mex_/travel/wdevlin/wdpinatahistory.html.