a symbol of Islamic identity in common usage. However, this symbol did not, in fact, rise from religious sources. This symbol first came into use with Muslims when the Turks conquered Constantinople. The crescent symbol was popular among the Byzantines then and the Turks later adopted it. Different countries have since used the symbol to indicate Muslim origins, etc., attributing various meanings to the crescent and star.
If you're referring to mosques and Islamic flags, it predates Islam when pre-Islamic people (Arabs) worshiped a crescent moon god father of which many statuettes have been found throughout the Middle East. Mecca is where this god being supposedly resided. These pre-Islamists also worshiped a female sun goddess and several 'star' daughters as well as meteorites that would occasionally fall, one of which was incorporated into the Kabba around which modern Muslims worship. This is also probably why they follow a lunar based calendar and carry small swords shaped like crescent moons. Some say one of the names of this moon god was "Allah" but others argue that Allah just means "god". But it's quite likely Mohammed & his followers assimilated pagan traditions and beliefs with his new found faith.