Using interferometric methods, radio astronomers have shown that very rapid motions involving radio jets are detectable in a variety of active centers: the nuclei of low-redshift radio galaxies, QSOs and BL Lac objects, and active binary systems containing a black hole or a neutron star in our own Galaxy. By comparing the positions of about 80 extragalactic sources of this type with the position of the galaxies in the de Vaucouleurs catalog and the updated QSO catalog of Véron-Cetty and Véron, it is shown that about 50% of them lie within 1° of a low-redshift spiral galaxy, and about 15% lie so close to galaxies (∆θ<=10') that the associations are highly significant. Thus, the sources are probably physically associated with these galaxies. All the galaxies are classified as spiral. In addition, many of the sources have other QSOs lying very close to them. These results suggest that the motions observed in these radio sources, as well as in the nuclei of radio galaxies and in Galactic microquasars, and perhaps in many more QSOs and other objects, are all similar and are mildly relativistic, and they do not require us to invoke large Lorentz factors. Some of the problems associated with this picture are discussed.