This article is from the Model Rockets FAQ, by Wolfram von Kiparski with numerous contributions by others.
DOT (Dept. of Transportation) regulates shipping of rocket motors and
CPSC (Consumer Products Safety Commission) regulates what may and not
be sold as a 'consumer' items at the retail level.
FAA (Federal Aviation Administration) is responsible for airspace
control and regulates flights of rockets that exceed 1 pound and
enter FAA regulated airspace.
NFPA (National Fire Protection Association) makes recommendations for
use of non-professional rocket motors. Although the NFPA only
makes recommendations, most state and local laws concerning the
use of model rockets are based, at least in part, on NFPA
recommendations; especially NFPA 1122. The NFPA also has a draft
definition and safety code for High Power rockets, NFPA 1127.
BATF (Bureau of Alcohol, Tobacco and Firearms) has responsibility for
regulations concerning storage and use of explosives. This agency
has taken a recent interest in looking into how high power rocket
motors are stored and used.
ATC (Air Traffic Control) You must notify the nearest FAA ATC center
prior to flying Large Model Rockets or High Power Rockets.