|Some dare call it|
Black helicopters are to the 1990s what snake oil was to the age of traveling salesmen pushing patent medicines, in that it is an example of a term that was seriously used by proponents but was so preposterous that the term took on a life of its own as a means of ridicule.
Allegedly, the United States government and/or the United Nations were preparing fleets of unmarked black helicopters which were to become the means of military occupation of the United States in the name of the New World Order. This was first seriously proposed by Mark "from Michigan" Koernke and Linda Thompson circa 1993-1994 in their videos America Under Siege (Thompson) and America In Peril (Koernke). The book Black Helicopters Over America by Jim Keith followed shortly thereafter. Talk radio hosts picked up the term from there mostly to ridicule the idea and it took on a life of its own, largely as an ironic joke through talk radio and the internet.
The inspiration for this theory may come from the ones seen in the film Capricorn One, where they are used by the US government to chase down three astronauts trying to reveal that their mission to Mars was faked. The helicopters in the film behave more like sentient beings in their own right rather than vehicles, sometimes turning to face each other for no apparent reason other than pure dramatic effect.
 Helicopters, but not as we know them
Black helicopters are said to be able to perform all kinds of manouevers that ordinary helicopters cannot, as well as having a silent mode. (Somehow, those of us who have lived near airports wish all helicopters had this facility!) Others have them as being unmanned drones.
Not all black helicopter fans support the UN/NWO idea. A rival theory has it that they are in fact alien spacecraft in disguise. Sometimes this is mixed in with the NWO angle. Sometimes they're sighted near alleged cattle mutilation sites (either as perpetrators or as investigators.)
It's pretty much the aerial analogue to the Men in Black phenomenon.
 Pop culture
The term has since been used almost exclusively in an ironic or sarcastic way to refer to any conspiracy theory which is particularly absurd and improbable. Black helicopters don't play much of a role in serious conspiracies any more, as the idea of perfectly silent helicopters flying about at night for no particular reason is a bit superfluous. Even despite that, some Internet cranks who experiment with "Orgone energy" claim that they are being stalked by low-flying black helicopters. Their hypothesis is that their Orgone accumulators are generating a frequency that the Government/New World Order is trying to track. The same frequency, they claim, stops HAARP, and cures cancer, and creates rain, blah blah blah...
Black helicopters also feature prominently in the Mel Gibson vehicle, Conspiracy Theory.