Only a few festae are still celebrated in Rome, and he biggest is on December 8, the feast of the "Immaculate Conception" (conception without "original sin") of Mary, the mother of Jesus. The festa is celebrated in the southern extension of Piazza di Spagna, actually Piazza Mignanelli, and the focus is on the enormous column, topped with a statue of Mary, that Pope Pius IX dedicated and blessed in 1857. Observances take place throughout the day, but the festa really gets rolling in late afternoon -- the Pope is scheduled to make his annual visit to the piazza at 4 PM and, after putting flowers at the base of the pillar, he will lead the crowd in prayer. (He then will go to St. Mary Major for another observance of the feast.) While the religious part of the festa is celebrated in Piazza Mignanelli, food vendors and street entertainers are in the northern end of Piazza di Spagna and surrounding streets. Separating the religious from the secular are large floral decorations in the center of the piazza.
If you have lots of energy and a high tolerance for crowds, you can do as many Romans do, and visit this festa in Piazza di Spagna and the opening of the Christmas fair in Piazza Navona on the same day.
Christmas Fair -- Piazza Navona: The Christmas Fair at Piazza Navona also begins on December 8, and it runs until the feast of the Epiphany in January. There are booths with toys, Christmas decorations, figures for Christmas nativity scenes, candies, cakes, and such traditional goodies as giant sugar doughnuts and hot roasted pork sandwiches. All of Rome's clowns, mimes, puppeteers, and street entertainers seem to show up along with a few of the traditional Italian bag-pipers in rustic costumes. A wonderful merry-go-round enthralls the kids. The fair is popular with Italians as well as with the foreign community, and sometimes the Piazza can be wall-to-wall with people. A visit on December 8 will immerse you in a vast crowd, and Saturdays and Sundays are also crowded. (Watch out for pickpockets!) After dark the Piazza is a fairyland of lights and that's when it's most fun to go.
You will want to know what's around you on the famous piazza:
The Fountains (includes an old photo of the annual flooding of the Piazza): http://pub.xplore.it/nerone/nerone/thismont/giugno/navona.htm
Piranesi's drawing of the Piazza: http://www.siba.fi/~kkoskim/rooma/pages/PIRA010B.HTM
G. Falda's drawing of Borromini's S. Agnese Church: http://www.siba.fi/~kkoskim/rooma/pages/FALD306B.HTM
S. Agnese Church -- Morlacchi http://www.bestitaly.net/morlacchi/01b.htm
Palazzo Pamphili (next to S. Agnese) -- Morlacchi: http://www.bestitaly.net/morlacchi/01a.htm
And how do I know the Pope's December 8 schedule? I look at his official calendar of religious events at: http://www.vatican.va/news_services/liturgy/documents/ns_lit_doc_20000927_calendar-aug-dec_en.html