Data are presently available on the luminosities and half-light radii of 101 globular clusters associated with low-luminosity parent galaxies. The luminosity distribution of globulars embedded in dwarf galaxies having $M_{v} > -16$ is found to differ dramatically from that for globular clusters surrounding giant host galaxies with $M_{v} < -16$. The luminosity distribution of globular clusters in giant galaxies peaks at $M_{v} sim -7.5$, whereas that for dwarfs is found to increases monotonically down to the completeness limit of the cluster data at $M_{v} sim -5.0$. Unexpectedly, the power law distribution of the luminosities of globular clusters hosted by dwarf galaxies is seen to be much flatter than the that of bright unevolved part of the luminosity distribution of globular clusters associated with giant galaxies. The specific frequency of globular clusters that are fainter than $M_{v} = -7.5$ is found to be particularly high in dwarf galaxies. The luminosity distribution of the LMC globular clusters is similar to that in giant galaxies, and differs from those of the globulars in dwarf galaxies. The present data appear to show no strong dependence of globular cluster luminosity on the morphological types of their parent galaxies. No attempt is made to explain the unexpected discovery that the luminosity distribution of globular clusters is critically dependent on parent galaxy luminosity (mass?), but insensitive to the morphological type of their host galaxy.