The fasts that all Jewish people are obligated to fast every year (other than Yom Kippur) are on: the 9th of Ab, the 17th of Tammuz, the 3rd of Tashri (Som Gedaliah) and the 10th of Tebeth.
Through these fasts that were established by our Rabbis of blessed memory, we remember what befell us and we understand that our sins are what brought this exile upon us. If it were not for these fasts, we would have forgotten by now all that transpired and we would not be moved to return to the right path.
As a result of these fasts that return every single year, however, we are conscious of the fact that repentance is the remedy for all our that has befallen us. And through it we will merit to receive all the good of this world and the world to come and see the coming of Mashiyah Sidqenu (the Messiah), speedily in our days, Amen.
(See Shulhan 'Arukh, 549:1. Sh. 'A. H' Rafael Barukh Toledano, 496, Oth 9)
