In addition to Yom Kippur, The Talmud (Tractate Rosh Hashana 18b) discusses four fast days (based on Zechariah 8:19) that commemorate the destruction of the First and Second Temples and the exile of the Jewish People from their homeland. In addition, two other fast days are mentioned in the Rabbinical literature, yielding a total of six tzomot (seven if Yom Kippur is included). The following list shows the seven fast days of the Jewish year, from the first fast of the year to the last:
Ta'anit Bechorim - The Fast of the Firstborn is a fast observed only by firstborn males, commemorating the fact that they were saved from the plague of the firstborn in Egypt. It is observed on the day before Pesach (Nisan 14).
Tzom Tammuz - Fast of the 17th of Tammuz. In Jewish tradition, Moses smashed the tablets on the seventeenth day of the fourth month (Tammuz), after he came down from Sinai and found the people worshiping the Golden Calf. This tragedy was seen as prophetic, since it was on this same date that the walls of Jerusalem were smashed by the invading armies of Nebuchadnezzar (see 2 Kings 25:2-7), an event which led to the destruction of the Temple and the exile of the people three weeks later, that is, on the ninth of Av. In the Bible, this is referred to as the Fast of the 4th month.
Tishah B'Av - The Ninth of Av, a fast day remembering the tragedies of the Jewish people (July/Aug). In the Bible, this is referred to as the Fast of the 5th month. Note that many people also fast on the first of Av, since this is the yahrzeit of Aaron the High Priest. The Fast of Tishah B'Av is the second most important fast in Judaism (next to Yom Kippur, which is the most important fast day). On the eve of the Tishah B'Av fast, it is customary to eat a boiled egg sprinkled with ashes...
Tzom Gedaliah - The fast right after Rosh Hashanah (on Tishri 3) commemorating the murder of the Judean governor Gedaliah by misguided zealots (Sept/Oct). In the Bible, this is referred to as the Fast of the 7th month.
Yom Kippur - The Day of Atonement (Tishri 10) is the most holy day of the Jewish year. This a fast day where no work of any kind is permitted. Note that Yom Kippur is the only fast day mentioned in the Scriptures for the purpose of teshuvah (repentance). So important is this fast that it is permitted even when it falls on a Shabbat (unlike other fast days that are postponed if they fall on the Sabbath).
Asarah B'Tevet - The 10th of Tevet, a fast day commemorating the fall of the Jerusalem. In the State of Israel, Kaddish (the Jewish prayer for the deceased) is recited on this day for people whose date or place of death is unknown (Dec/Jan). In the Bible, this is referred to as the Fast of the 10th month.
Ta'anit Esther - The Fast of Eshter is observed on the day before Purim, on Adar 13 (in Feb/Mar).
Other Fast Days
Besides the seven traditional fast days that are universally recognized within the observant Jewish community worldwide, there are some additional fast days within Jewish tradition that should be noted. These include:
Ta'anit Tzaddikim - "Fast of the Righteous ones." These are fasts in memory of an outstanding person who demonstrated the life of faithfulness to God (i.e., yahrzeit fasts). Some of these fasts include:
The Fast of Miriam - 10th Nisan
The Fast of Aaron - 1st of Av
The Fast of Moses - 7th of Adar
The Fast of Joshua - 26th of Nisan
Fast of Samuel - 28th of Iyyar
Ta'anit Tzibur - These are fasts instituted by a particular community in memory of a special deliverance (purim) or the death of a revered community leader.
Ta'anit Yachid - "Personal fast" or "unique fast." This is a fast performed in private for the sake of a personal need or request (bakashah).