Yule is usually held to celebrate the longest night of the year, and the eventual return of the sun. Often a vigil is held the entire night to welcome the sun in the morning -- similar to New Years Eve. Light is an important part of the holiday, so a fire or grouping of candles is usually maintained.
(See below for more common traditions). 

Common Traditions
There are many traditions that seem to be cross-cultural -- they are used similarly by Wiccan, Asatru, Druidic, and eclectic groups. The names or symbolism may change from group to group, however. 

Many groups burn Yule Logs to keep the light alive all through the long night. Quite often the Yule Log is the remains of the May Pole from that years Beltane. Sometimes the Log itself is not burned -- instead, candles are arranged on it and kept lit all night long. In many traditions, everyone stays up all night to watch the fire and then welcome the sun back in the morning (although in some only one person will remain awake
with the fire). 

Mistletoe, Holly, and Evergreen are all important plants of the season. Often, houses are decorated with them, symbolizing life in the dead of winter. 

Many groups include the fall of the Holly King and the rise of the Oak King. The Holly King represents the Dark Half of the Year. At Yule, he loses battle to his brother/alter ego/father/etc the Oak King, who represents the Light Half of the Year. 

Specific Traditions

Druid
According to the ADF webpage, "the Celts did not celebrate Solstices or Equinoxes." But, it seems that most Druidic organizations usually celebrate the holiday anyway. (Here is the ADF liturgy for Yule, by the way). Common themes to the different rituals are a yule log and a celebration of the rebirth of the sun. 

Asatru (according to The Troth)
Yule is a very important (possibly the most important) holiday in Asatru. It is easily comparable to another Pagan holiday, Samhain, in that it focuses on the dead and the coming year. The traditional Yule season is thirteen days long, from the night before the actual Solstice until twelve days later. The most important night of the Yule season is the longest night itself. On that night, the Yule Log is burned and there is an all night (or at least late night) feast. 

Another custom that links Yule to Samhain through the Asatru tradition is the Wild Hunt. Through the Yule season the Wild Hunt rides, bringing with it the souls of the departed. Because of this the Yuletide season is considered outside normal time. No work is attempted, especially work which includes turning wheels, such as spinning or grinding. The dead are said to return to their families to check up on them and take part in the festivities.