Below I list calendar dates and specific times of the year which are associated with fasting. In addition, communities or individuals may fast at other times (e.g. in times of trouble, after having a bad dream, on a parent's yahrzeit, on one's wedding day) which are not associated with any particular time of year.
For ease of reading, I have broken the fast days out into a number of categories of my own devising, some of which are arguable. I also list sources, reasons for those specific dates, along with rules specific to only certain fasts.
Unless stated otherwise, it is generally assumed that fasts begin at daybreak. In general, the fasts are assumed to apply to healthy adults (males over age 13 and females over age 12). Aside from Yom Kippur, there are four rabbinically mandated days where all healthy adults must fast. For all other fasts, only those who have accepted the fast (either via explicit declaration or in some circumstances implicitly due to widespread, communal or personal custom) will do so.
Biblically mandated fasts
- 10 Tishri (Yom Kippur) - applies to all adults who are not deathly ill, fast begins at sunset the previous day, also forbidden to bathe, anoint, wear shoes or engage in marital relations, fast takes place even on shabbat
Rabbinically mandated fasts
(commemorating aspects of the churban along with other tragedies, OC 549:1)
- 3 Tishri (Tzom Gedalya) - assassination of Gedalya
- 10 Tevet - start of siege of Jerusalem
- 17 Tammuz - walls of Jerusalem breached
- 9 Av - destruction of Temple - fast begins at sunset the previous day, also forbidden to bathe, anoint, wear shoes or engage in marital relations
If any of these dates are shabbat the fast takes place on the next day (Sunday).
Customary fasts connected to holidays
- Monday-Thursday-Monday (BeHaB) in Marcheshvan (OC 492) - after the first shabbat after Rosh Chodesh Marcheshvan (some wait until 17 Marcheshvan to start). Some continue fasting Mondays and Thursdays until Chanukah (Kol Bo 61:1).
- 13 Adar (II) - Ta'anit Esther (OC 686:2) - If it falls on shabbat then it takes place on the Thursday before (in some rare circumstances possibly on the Friday before).
- Monday-Thursday-Monday after Purim (OC 686:3, MB 686:8) - to commemorate Esther's three days of fasting
- 14 Nissan - Ta'anit Bechorot (OC 470) - only applies to firstborn males (some say even female firstborns) - if it falls on shabbat then it takes place on the Thursday before (although some say that it is skipped that year).
- Monday-Thursday-Monday in Iyar (BeHaB) (OC 492) - after the first shabbat after Rosh Chodesh Iyar. Some continue fasting Mondays and Thursdays until Shavuot (Kol Bo 61:1).
- Monday-Thursday-Monday after Shavuot (Kenesset HaGedolah 492)
Customary fasts at times linked to repentance
- Forty days of fasting leading up to Yom Kippur, starting after 17 Tammuz (Baer Heitev OC 581:10) (Some start after 15 Av (Mateh Ephraim 581:2))
- First day of selichot (minhag ashkenaz) (MB 581:15)
- 29 Elul (Erev Rosh Hashanah) (OC 581:2)
- During the Ten Days of Repentance (apart from shabbat shuvah and erev yom kippur) plus four days before Rosh Hashanah to give a total of 10 fasts (OC 581:2, MB 581:6)
- Erev Rosh Chodesh (Yom Kippur Katan) (MB 417:4) - apart from Erev Rosh Chodesh (Tishri), Marcheshvan, Tevet and Iyar. If it falls on shabbat the fast is moved earlier to Thursday, if it falls on Friday some also move it to Thursday.
- Regular Year: Thursdays of the weeks of shovavim (Shemot through Mishpatim) (Sha'arei Teshuvah 685:2)
- Leap Year: Thursdays of the weeks of shovavim tat (Shemot through Tetzaveh) (some include also Vayakhel and Pekudei) (MA 585)
Customary fasts commemorating events and tragedies
- 5 Tishri - death of 20,000 Jews and capture of R. Akiva (OC 580:2)
- 7 Tishri - decree of death following the golden calf episode (OC 580:2) (MB - some have 6th)
- 7 Marcheshvan - blinding of Tzidkiyahu and execution of his sons (OC 580:2) (MB - some have 6th)
- 28 Kislev - Yehoyakim burnt the prophecy of Yirmiyahu (OC 580:2)
- 8 Tevet - Torah translated into Greek (OC 580:2)
- 9 Tevet - an unspecified disaster (OC 580:2) (MB - death of Ezra)
- 5 Shevat - death of Elders in days of Yehoshua (OC 580:2) (MB - some have 8th)
- 23 Shevat - battle against the tribe of Binyamin (OC 580:2)
- 7 Adar - death of Moshe (OC 580:2) (MB - in a leap year common custom is to observe in Adar I)
- 9 Adar - split between Beit Shammai and Beit Hillel (OC 580:2)
- 1 Nissan - Death of Aharon's sons (OC 580:2)
- 10 Nissan - Death of Miriam (OC 580:2)
- 26 Nissan - Death of Yehoshua (OC 580:2) (MB - some have 28th)
- 10 Iyar - Death of Eli and his two sons, capture of the Aron (OC 580:2)
- 28 Iyar - Death of Shemuel (OC 580:2) (MB - some have 29th)
- 1 Sivan - First Crusade (1096), custom of Worms community (MB 418:1)
- 20 Sivan - Blois blood libel (1171), Rintfleish Pogrom (1298), Chmielnicki Massacres (1648-49), observed by males over 18, females over 15 (MB 580:16)
- 23 Sivan - Yerov'am prevented the people from bringing bikkurim (OC 580:2)
- 25 Sivan - Death of RaShBaG, R. Yishamel, R. Chanina Segan Hakohanim (OC 580:2)
- 27 Sivan - Burning of R. Chananya b. Teradyon with a sefer torah (OC 580:2)
- Friday of Parashat Chukat - burning of the Talmud in France, destruction of communities in Poland in 1648 (MB 580:16)
- 17 Tammuz until 9 Av - churban (OC 551:16) (hat-tip @DoubleAA)
- 1 Av - death of Aharon (OC 580:2)
- 10 Av - the Temple continued to burn (MA 558:3)
- 18 Av - Extinguishing of ner hamaaravi (OC 580:2) (MB - some have 17th, good to fast on both)
- 17 Elul - death of the spies (OC 580:2) (MB - some have 7th)
Certain days of the week
- Mondays and Thursdays (OC 580:3) - destruction of the Temple, burning of sifrei torah, desecration of G-d's name
- Fridays (OC 249:3) - to have appetite for the shabbat meal
Fasts for rain in Israel
- Up to 16 fasts, starting from 17 Marcheshvan, held on Mondays and Thursdays (OC 575)
Fasts for astronomical phenomena
- At the time of a (solar or) lunar eclipse (Sefer HaChassidim 230, MB 580:2) (hat-tip @DoubleAA)
Fasts of the Chevra Kadisha
Held on different dates in different communities; popular choices include:
- 15 Kislev
- 29 Tevet
- 29 Shevat
- 7 Adar (II, although some do Adar I)
- 29 Adar (II)
(See Nit'ei Gavriel Hilchot Aveilut II:98 for a comprehensive list of Chevra Kadisha fast days in various communities)