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It is a very widespread custom to observe the Hebrew anniversary of a parent's death, yahrzeit (from the German, yahr, "year", and zeit, "time"). It is common to light memorial candles and say prayers in shul; some visit the grave. There is a custom to fast on a yahrzeit; on the other hand many, particularly in Israel, make a family meal.
Yahrzeit observance seems to have become established in the Middle Ages, though Rashi finds a source for it in the Talmud (Yevamot 122a). Interestingly, until modern times it was a predominantly Ashkenazi custom, not widely followed among Sephardi Jews. Rabbi Yosef Kapach, the great 20th century Yemenite-Israeli scholar, was once asked how he observed a yahrzeit. "Following Maimonides customs," he answered. The questioner searched through Maimonides's books and returned to Rabbi Karpach, complaining that he found nothing there about how to observe yahrzeit. "Exactly!" replied the rabbi.