We present a statistical analysis of the properties of galaxies containing ultraluminous X-ray objects (ULXs). Our primary goal is to establish the fraction of galaxies containing a ULX as a function of ULX luminosity. Our sample is based on ROSAT HRI observations of galaxies. We find that ~12% of galaxies contain at least one ULX with L_X > 10³⁹ ergs s^-1, and ~1% of galaxies contain at least one ULX with L_X > 10⁴⁰ ergs s^-1. These ULX frequencies are lower limits, since ROSAT HRI observations would miss absorbed ULXs (i.e., with N_H 10²¹ cm^-2) and those within ~10'' of the nucleus (due to the positional error circle of the ROSAT HRI). The Hubble type distribution of galaxies with a ULX differs significantly from the distribution of types for nearby Third Reference Catalog galaxies but does not differ significantly from the galaxy type distribution of galaxies observed by the HRI in general. We find no increase in the mean far-infrared (FIR) luminosity or FIR/K-band luminosity ratio for galaxies with a ULX relative to galaxies observed by the HRI in general; however, this result is also most likely biased by the soft bandpass of the HRI and the relatively low number of high star formation rate galaxies observed by the HRI with enough sensitivity to detect a ULX.