Federal Emergency Management Agency
It provides federal relief to areas afflicted by natural disasters, and has drawn a great deal of criticism for its face-palming incompetence in doing so, which is largely a result of being used as a dumping ground for political lackies too important to ignore (but not important or dangerous enough to make Secretary of State) than any incompetence of the members themselves.
FEMA was originally a weird bureaucratic anomaly since it was created by a series of executive orders rather than by an act of Congress. In 2002 it was finally codified into law and made a component of the Department of Homeland Security. As well as providing large scale emergency management FEMA is also the largest flood insurer in the United States, mainly because most insurance companies don't offer it since it is generally expensive.
FEMA has been the focus of a great number of nutbar conspiracy theories. Many of them center around Mount Weather, their headquarters in Virginia, which is a sort of spare Washington, D.C. (in case the real one gets nuked) and the purported location of the US Shadow Government! FEMA also supposedly has the power to declare martial law and round up half a million American citizens into concentration camps so that the UN can take away everyone's guns, once someone gives them a map and a flashlight so they can locate their own asses.