In 1954, at the height of the Cold War (and 16 years before the shoe company of the same name appeared), the United States Department of Defense introduced a new missile defense system. The system, unlike ones before it, was a guided missile system, with a range to defend cities from up to 75 miles away by the program's end.
The first Nike incarnation was the Ajax. Effective up to 25 miles with a top speed of Mach 2.5, they were used from the program's start into the mid-1960s. They carried normal explosive warheads. In 1958, the upgraded Hercules missile was introduced, which increased range to 75 miles, increased speed to Mach 3.6, and added nuclear capability.
Nike sites were deployed as a ring around several large, important cities; for example, New York City had no less than 19 sites surrounding it, and Washington, D.C. had around a dozen of them, scattered amongst the suburbs. With the coming of SALT I in the early 1970s, the Nike sites were decommissioned. Most of them were simply abandoned; one of the sites on the Lorton Reformatory complex was converted into a jail. One site in the San Francisco area, SF-88, was transferred to the National Park Service for future use as a museum, and in 1984, the Military Vehicle Collector's Club began restoring it. It's now open for tours.
While their days in the US are over, the system still see use elsewhere. South Korea still has 200 Hercules missiles in full service.
Sources: http://www.nikemissile.org and http://ed-thelen.org