In General
Anywhere on an aircraft's flight path, the FAA stipulates that altitude should never be so low that an emergency landing in the event of an engine failure would endanger persons or property on the surface. Excessively low altitudes make accurate, unpowered glides to safe landing spots less viable.
Over Congested Areas
Over congested areas, which could mean a city or a populous open-air event such as a football game, the FAA requires a minimum safe altitude of 1,000 feet above the highest obstacle within 2,000 horizontal feet of the aircraft. Over high-density urban areas with tall buildings, this would require a substantially higher altitude than merely 1,000 feet above ground level.
Over Non-Congested Areas
Above non-congested areas, an altitude of 500 feet or more must be maintained. For flights over open water or sparsely populated land, the FAA minimum safe altitude regulation states that the aircraft may not pass within 500 feet of a person, vessel, vehicle or structure. The 500 feet may be measured vertically, horizontally or at an angle.
Helicopters
Because helicopters have the capability to hover, the FAA grants them a considerable exception to minimum safe altitude rules. Helicopters may operate below the minimums provided they are not endangering persons or property on the ground and as long as they are in accordance with any specific routes or altitudes prescribed by the FAA in particular areas, such as controlled airspace over cities or around airports.