With one exception, the host galaxies associated with GRBs observed to date lie in the magnitude range 24.4<=R<=25.8. Here we compare the observed redshifts and magnitudes of the host galaxies with the predictions of three basic models: the comoving rate density of GRBs is (1) proportional to the cosmic star formation rate density, (2) proportional to the total integrated stellar density and (3) constant. At any epoch, the probability of a GRB occuring in a galaxy is assumed to be proportional to that galaxy's broad-band luminosity. No assumption is made of standard candles or even a narrow GRB luminosity function. The integrated stellar density model is ruled out. The star formation and constant models are consistent with the observed GRB host galaxies to date; these two models make very similar predictions for host magnitudes and redshifts but can be distinguished by the average spectral properties of the host galaxies. The peak in the distribution of host magnitudes in these models is predicted to be near 25 mag, but the width of the distribution in any model is broader than the observed width; this suggests that some associations of GRBs with hosts may be spurious. All models predict that at least a third of future host galaxy detections will be brighter than 24 mag. The fraction fainter than 26 mag constrains the faint end of the galaxy luminosity function at high redshift, if the bursters are not expelled from low-luminosity hosts. In all models, the probability of finding a z<0.008 GRB among a sample of ten GRBs is less than 10^{-4}, strongly suggesting that GRB 980425, if associated with supernova 1998bw, represents a distinct class of GRBs.