Mysterium Lunae

Don Jim Tucker links to some resources on the crescent moon as symbol of Islam.
The crescent moon is also associated with Our Lady - sometimes she is shown standing atop a crescent moon, but I've also seen a crescent used on its own as her symbol. This page gives a brief overview of the meaning of the crescent in the Christian context:

Patristic times saw in the symbol of the moon, or the "mysterium lunae", i.e. the three phases of the moon: dying (waning), generating (waxing) and giving birth (full moon) a valid representation of the Church (ecclesia). Ecclesia is virginal and"dying" in the encounter with Christ, the bridegroom; she is maternal and lifegiving in her spousal relation with the redeemer, and resplendent in her grace-filled existence.
John the Baptist is sometimes connected with the waning moon (Baptistry of Östr Hoby, Sweden, 12c) to explicate his role as the last prophet of the waning Old Testament which is regarded, simultaneously, as a promise of the New Testament. The moon contrasts here the sun as symbol of fulfillment, in other words, the New Testament, more specifically Jesus Christ himself, the sol invictus. The same contrast is used to signify ecclesia and synagoga. The latter is identified with the symbol of the waning moon.
Mary as the God-bearer is identified with ecclesia. She is standing on the waning moon which points out that the Old Testament and synagoga are the foundations of the Church. No doubt that we have here also the idea of victory of ecclesia over synagoga. The motif of the luna is very old (~820, MS 99 Paris, Valenciennes) and is not used in the beginning as an attribute of Mary but of the Church. It is only in the 14/15c that a lateral transfer takes place, meaning Mary occupies now in iconography the place of the Church and inherits some of its attributes. The Katharinenthal Gradual of 1312 shows an image of transition, where the same feminine figure contains or bears the attributes of the Church, Mary and the Apocalyptic Woman. The figure stands on a personalized half moon. It is true that the visual elements, half moon, stars, sun, are borrowed from Revelations 12,1. Early representations of Ecclesia (10-12c) show her as the apocalyptic woman with the dragon. The motif of the apocalyptic woman is applied in a variety of ways to Mary.