The old testament has a story relating to this question. Exodus 1:15-21 ( in my translation, available on Wikisource,
And the king of Egypt said to the Hebrew midwifes, one of whose names is Shiphrah, and the second Poo'ah. And he said, "When you deliver for the Hebrews, and you saw upon the paired rocks, if it is a son, and you killed him, and if it is a daughter, she lives." And the midwives feared God, and did not do that which the king of Egypt commanded, and they let live the boys born.
And the king of Egypt called the midwives, and told them "Why did you do this thing, and let the boys born live?" And the midwives told Pharaoh that the Hebrews are not like the Egyptian women, that they are animals, not even does the midwife arrive, and they have delivered. And God made good for the midwives, and multiplied the nation, and they became very mighty. And it was because the midwives feared God that he made households for them.
Here, the midwives say that the Hebrew women are like animals, not needing a midwife. This is an obvious lie, and it is a useful lie, because it allows the midwives to save the boy babies. God rewards the midwives financially for this.
In traditional translations, the midwives statement is translated to "the Hebrew women are very lively, they deliver before the midwife arrives". This mistranslates the word "Chayoth", which means "animal" by substituting a different meaning, which is a feminine adjective meaning lively, which is both a painfully stretched interpretation and completely spoils the beautiful and jarring sentiment. This sentence reveals a lot about Pharaoh's Egyptian supremacy ideas--- he is willing to believe any demeaning fact about the Hebrews. This is a biblical parallel to the Nazi-hiding example used in Matt White's answer.
The midwives lie for the purpose of a greater good. Exodus does not ask people to be stupid, and if they have to lie to the authorities, this can sometimes be a good thing. Established religion is authoritarian, so it is not a good interpreter of the holy texts, which are written by inspired authors. This passage is both mistranslated and ignored by Christians and Jews alike.