In the Vatican (as in the East), it continues to be celebrated on January 6, even as in many parts of the world (including Rome and all of Italy, I think, and the United States), the fest is translated to the nearest Sunday.
And of course there are some fascinating customs associated with this feast.
In Bulgaria, young men dive into frigid waters to touch a cross, which has been thrown in to bless the waters. This is a practice common to many Orthodox countries, including Greece.
There's the Three Kings Parade in New York. The gift-giving tradition at Epiphany is also followed in the Philippines.
Gift-giving and parades are also part of the celebratin of Epiphany in Spain.
In Italy, a wizened witch, La Befana (a corruption of "Epiphania") brings gifts to little children.
In Ethiopia, they celebrate Timkat. According to Ethiopian tradition, the Three Kings brought the gift of the Arc of the Covenant to Ethiopa. Here's a YouTube video with a some documentary footage on Timkat, including some beautiful liturgical chanting. (The Ethiopian Orthodox still follow the Julian calendar, so Timkat falls during the third week of January).
From the Pope's homily today (Asianews):
On the day when the Church celebrates the manifestation of Christ to the gentiles, represented by the Magi who came from the East, Benedict XVI launched a heartfelt appeal to “today’s Magi”: politicians, scientists and representatives of non-Christian religions, that they may discover that Christ is the fulfillment of their searching. In the setting of St Peter’s Basilica, in a Eucharistic celebration, with Asian, African, Polynesian ministrants, the pontiff presented the message of the Epiphany once again, of a “God who revealed himself in history as the light of the world, to lead and finally to introduce mankind to the promised land, where freedom, justice and peace reign”. To “today’s Magi” and “to all men of our time”, the pope repeated: “Do not be afraid of the light of Christ! His light is the splendour of truth. Let yourselves be illuminated by Him, all peoples of the earth, allow yourselves to be covered by his love and you will find the path of peace.”You have revealed Yourself to the world today, and Your light, O Lord, has shined upon us. We recognize You and exclaim to You: "You have come and revealed Yourself, O Inaccessible Light. (Kontakion of the Theophany, from the pages of Epiphany Byzantine Catholic Church, Roswell GA). [Photo credits: Yahoo News and CNN]