mid-15c., "group of soldiers sent as reinforcements" (a sense now obsolete), from Old French crue, creue "an increase, recruit, military reinforcement," from fem. past participle of creistre "to grow," from Latin crescere "to arise, grow" (from PIE root *ker- (2) "to grow"). Compare accrue.
Meaning "any company of people" is from 1570s; that of "group of people engaged upon a particular work" is attested by 1690s. Sense of "company of seamen who man a ship, vessel, or boat, common sailors of a ship's company" is from 1690s. Crew-cut hairstyle first attested 1938, so called because the style originally was adopted by boat crews at Harvard and Yale.