The
G stands for
Government, as
FBI agents work directly for the
U.S. Federal Government rather than a local
police department.
The term was allegedly coined by gangster George "Machine Gun" Kelly1 in September 1933. While being arrested by DOI agents (Division of Investigation, a precursor to the FBI), Kelly yelled at them Don't shoot G-men, don't shoot.
1http://www.fbi.gov/libref/historic/history/historicdates.htm