This depends on where you are traveling. If you are traveling domestically, then no passport is required, but other ID may be requested. If you are traveling internationally, then yes. All children under 16 much have their own passport in order to travel internationally.
Source for information: TSA Passport Minors.
• Minors under age 16 must apply in person
• There are special requirements for All Minors Ages 16 & 17
• All minors regardless of age, including newborns and infants, must have their own passport when traveling internationally by air.
U.S. and Canadian citizen children under age 16 arriving by land or sea from contiguous territory may also present an original or copy of his or her birth certificate, a Consular Report of Birth Abroad, a Naturalization Certificate, or a Canadian Citizenship Card.