We present an analysis of the properties of a sample of 18 metal-rich, low-redshift z(sub abs) much less than z(sub em) absorbers seen in low- and medium-resolution spectra obtained for the Quasar Absorption Line Key Project with the Hubble Space Telescope Faint Object Spectrograph (HST/FOS). For most of the C IV and Lyman-limit systems, observations in the optical wavelength range of the expected associated Mg II absorption are available. As at high redshift (z approximately 2), there are two subclasses of absorbers which are characterized by the presence or absence of MG II absorption. However, some low-redshift Mg II and Fe absorptions originate from regions optically thin to UV ionizing photons and thus, at low redshift, the low-ionization systems do not always trace high opacities, as is the case at high redshift. This implies that the mean ionization state of metal-rich, optically thin absorbing clouds falls with decreasing redshift, which is consistent with the hypothesis that the gas is photoionized by the metagalactic UV background radiation field. Two main constraints are derived from the analysis of the Lyman-limit sample, assuming photoionization models are valid. First, a low opacity to ionizing photons (tau(sub LL) approximately less than 1), as observed for several Mg II-Fe II systems at z approximately 0.5, sets limits on the ionization level of hydrogen, thus on the total hydrogen column density and the heavy element abundances, (Z/H) approximately -0.5 to -0.3. Second, the dimensions of individual Mg II clouds are smaller than at high redshift by a factor 3-10. At z approximately greater than 0.6, the O VI absorption doublet is detected in four of the five z(sub abs) much less than z(sub em) systems for which the O VI wavelength range has been observed, whereas the associated N V doublet is detected in only two cases. This suggests that the presence of a high-ionization O VI phase is a general property of z approximately 0.6-1 absorption systems, as is also probably the case at high redshift. These O VI absorbers can be ionized by the UV metagalactic field if their density is low, nH approximately less than 3 x 10(exp -4)/cc. The O VI phase would then be a homogeneous region of large extent, r approximately greater than 50 kpc. A detailed photoionization model of the z(sub abs) = 0.791 absorber toward PKS 2145+06 confirms the properties derived from the Mg II, C IV, O VI, and Lyman-limit samples. The galaxy causing this extensive metal-line absorption system has been identified, and its possible contribution to the UV ionizing flux does not substantially modify the value of the derived parameters. The heavy element abundances are about half the solar values. The O VI region has a density about 20 times lower than the Mg II clouds and a size of approximately 70 kpc. Alternatively, the high-ionization phase could be collisionally ionized and trace gas associated with a possible group of galaxies at the absorber redshift.