Basically there is a holiday every week, which is Saturday (Shabbat)! It starts from the sunset on Friday and ends in the evening of Saturday when it gets dark. Observant Jews are not allowed to work on Saturday. Therefore almost all the shops and restaurants in West Jerusalem are closed. Nevertheless, there are still some places open on Saturday, e.g. the Old City (except the Jewish Quarter), the Cinematèque, Israel Museum, Bible Land Museum, the Old Train Station and the Biblical Zoo.
Other important holidays include Rosh Hashana, Yom Kippur, Sukkot and Pesach. For a list of holidays, please refer to: http://www.timeanddate.com/holidays/israel/ Most of the religious holidays are like Saturday. For the memorial days (Holocaust Memorial Day, Memorial Day, Tisha B’Av) restaurants will be closed in the evening. During the week of Pessach, bread with yeast (“Hametz”) is not sold in the Kosher places already days before the holiday begins (this can include a much bigger variety of products than expected). On Yom Kippur everything is closed (including airport, land border crossings) and no traffic is allowed, except emergency services.