We have made high-resolution, high-sensitivity dynamic spectra of a sample of strong pulsars, primarily with the Arecibo radio telescope. We find that almost all the pulsars show low-level features in their dynamic spectra that have a high-Q signature in the transform domain. There, in the so-called secondary spectrum, we see parabolic arcs that have a predictable scaling with frequency. These features can be explained by interference between a compact (~2 mas) image core and a much broader and fainter halo. A variety of previously studied scintillation phenomena - tilted scintles, periodic fringing events, and criss-cross patterns - appear to be related to this parabolic arc pattern. Time variability in the phenomena, which we can track from the early 1980's until the present, is an important clue to their physical origin. Because the milliarcsecond image features are caused by scattering at kiloparsec distances, these phenomena provide a new tool for probing the interstellar medium on solar system size scales. Since the phenomena are high-Q but sensitivity limited, the SKA will provide powerful new capabilities for their study.