Non-fixed Fast Days
Judaism has communal fasts that are not on the yearly calendar and numerous occasions when individuals may choose to fast.
Excerpted from A Guide to Jewish Prayer with permission of the publisher, Schocken Books.
It is accepted practice for Jewish communities, in times of trouble and distress, to declare a public fast on a certain day or days, hoping that the power of prayer and charity, fasting and self-purification, will bring heavenly salvation. The Bible refers to this several times, e.g., "Blow, the trumpet in Zion, sanctify a fast… then will the Lord be jealous for His land and pity His people" (Joel 2:15-18).
Among other instances, the people of Israel fasted for salvation from the Philistines (I Samuel 6:6), when their fields were devastated by a plague of locusts during the period of Joel (1:14), and on the three-day fast called in support of Queen Esther's efforts to overturn Haman's decree in the time of King Ahasuerus (see Esther 4:16). The Mishnah declares that this should be done "for any trouble that comes upon the community" (Mishnah, Ta'anit 2:8). Tractate Ta'anit is devoted to the laws and customs for such fast days.
Occasional Public Fasts
Fasts held on occasions of public distress may be declared for universal observance, for one country, for one city, or even by one community within a city. There is no clear-cut definition as to what is considered proper cause for a public fast day, the matter resting with the judgment of the local Jewish religious court. Thus, it might sometimes happen that a fast day is declared in one place where the community has been harmed by a particular event, even though the same event may be fortuitous for another community.
There was a fixed sequence of public fasts, of progressively increasing severity, for a scarcity of rainfall, or drought, in the Land of Israel. If the rainy season began and rain did not fall, a series of fasts was held (as many as 13, on Mondays and Thursdays of each week), culminating in several as stringent as the fast on Tisha B'Av. During Temple times, there was also a special order of shofar blowing, an additional six blessings were inserted into the Amidah [central standing prayer], and there was even a Ne'ilah service [a closing service like the one at the end of Yom Kippur].
Although some of these rulings were recorded in the Shulhan Arukh [the major code of Jewish law],in fact, such a series of fasts has not been held for many generations, although even today public fasts are occasionally proclaimed because of a lack of rainfall.
On fast days held for public distress, the prayer services are the same as for any other public fast day, including Torah reading in the Shaharit[morning]and Minhah [afternoon] services. There are special Selihot for a fast declared for lack of rainfall, as well as a special prayer formulation inserted in the Amidah. There is likewise a special piyyut [religious poem] for a fast day held because of an epidemic of children's diseases.