NASA has flown a decidedly eclectic fleet of aircraft throughout its history. Some of the aircraft that it flies are unique because they are purpose built test aircraft. Others are acquired from a variety of sources, for example, Boeing provided the 1st built 737 to NASA for use as a testbed. NASA bases its fleet as shown below. The tail number indicates the home base of the aircraft:
400 Wallops Flight Facility Wallops Island, Virginia 500 Langley Research Center Hampton, Virginia 600 Glenn Research Center Lewis Field, Cleveland, Ohio 700 Ames Research Center Moffett Field, California 800 Dryden Flight Research Center Edwards, California 900 Johnson Space Center Houston, Texas
The list below is certainly not exhaustive (just what I have photographed). A definitive reference for NASA aircraft is Flying the Frontiers: NACA and NASA Experimental Aircraft (Arthur Pearcy)
Note that most of the military types also have US Air Force, US Army or US Navy serial numbers.