Mistletoe
Ancient Greeks first began the tradition of kissing under the mistletoe. The Romans adopted it as part of the Saturnalia feast and would sometimes settle wartime agreements underneath a mistletoe sprig, making it a symbol of peace. As an evergreen plant, it was also used as a symbol of abundance and fertility in Saturnalia decorations.
Caroling
During Saturnalia people would go singing door to door, but fortunately for us, caroling of today does not entirely mimic another Saturnalia tradition—running through the streets naked and singing. The latter is the reason that throughout the centuries Christian churches have wavered on their policies about caroling, with the idea that singing coincides with debauchery.
Gift Giving
The concept of giving gifts was an important part of Saturnalia. Usually the gifts were small trinkets, dolls, sweets and the like. Masters would also give gifts to their slaves (perhaps a precursor to the idea behind Boxing Day, when employers would give a gift to their servants the day after Christmas).
Taking Care of the Less Fortunate
Saturnalia was also a time of swapping places. Masters would trade places with their slaves, serving them at meals instead of the other way around (although the slaves would still have to cook the meals). This tradition, of masters serving servants, would continue for a time but eventually fell out of favor. Today we look for ways to help those who are needier than ourselves, with many working in soup kitchens on the holiday to feed the poor. In the UK, British officers traditionally serve the holiday meal to junior officers, with Prince Harry recently carrying on the practice.