FBI Special Agent Dale Cooper (Kyle Maclachlan) on Twin Peaks or
FBI Special Agent Fox Mulder (David Duchovny) on The X-Files?
Here's your fun-fact for the day:
"In FBI mythology, the nickname "G-Man" is held to have originated during the arrest of gangster George "Machine Gun" Kelly by agents of the Bureau of Investigation (BOI), a forerunner of the FBI, on September 26, 1933. Finding himself unarmed, Kelly supposedly shouted "Don't shoot, G-Men! Don't shoot, G-Men!""