The Regulators are a relatively new group in the Capital Wasteland, having appeared only in 2267 or so. They take it upon themselves to punish troublemakers and do their best to keep a semblance of peace wherever they are.
In the Capital Wasteland, they are led by Sonora Cruz and operate out of the Regulator HQ. Unlike the corrupt Regulators seen in the original Fallout, the (non-related) Regulators of the Capital Wasteland are truly just-minded and seek to punish evil.
If the player has the Lawbringerperk, they can trade fingers taken from the corpses of evil humans or (non-feral) ghouls killed by the player, for good Karma and 5 to 10 bottle caps depending on Karma level. The Regulators will also attempt to claim the bounty on the player's head if they have accumulated bad Karma by committing serious crimes, such as destroying Megaton or enslaving people in the Capital Wasteland, or by simply murdering people.
Regulator is the actual term for an official who maintains control and supervision of an area of public interest.  As a result, many armed groups, both vigilante and official, have been named "Regulators" throughout American history. One of the most notable groups in American history were the Regulators of the Carolinas around the time of the American Revolution.