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We present high-resolution (0.3-1.2 km s<SUP>-1</SUP>) spectra, obtained with the AAT UHRF and/or the KPNO coudé feed, of interstellar Ca II absorption toward 44 Galactic stars. For most stars in the sample, these new spectra are characterized by higher resolution, higher S/N, and/or wider velocity coverage than previously available spectra. As was found in a similar high-resolution survey of Na I absorption, the Ca II profiles show complex structure in many lines of sight. Multicomponent fits to the line profiles yield estimates for the column densities, line widths, and velocities for 417 individual interstellar cloud components; an analysis of the component separations suggests that we may have discerned only about 40% of the components actually present, however. The mean LSR velocities of the Ca II and Na I absorption are similar, but the Ca II velocity distribution is broader, due to outlying components seen only in Ca II. The Ca II line widths imply that at most 40% of the Ca II components in the present sample could arise in warm gas at T ≥ 6000 K. If most gas traced by Ca II is warmer than 500 K, then the turbulent velocities in that gas must generally be subsonic. In general, the Ca II component line widths are larger than those of corresponding Na 1 components seen at the same velocity, suggesting that the Ca II occupies a somewhat larger volume, characterized by a larger temperature and/or turbulent velocity, than that occupied by the Na I. Ca II absorption can arise both in cold, relatively dense gas, where Ca is typically heavily depleted onto grains and Ca II can be its dominant ionization state, and also in warmer, lower density gas, where Ca is less depleted but Ca II is a trace ionization state. The interplay between the strong effects of Ca ionization balance and Ca depletion, for different types of neutral gas, can explain the similarities between the line profiles seen for Ca II and for various dominant first ions of less depleted elements. High-resolution spectra of Ca II can thus be useful for interpreting lower resolution UV spectra of many other species found in neutral clouds. The ratio of the column densities of Na I and Ca II is not an unambiguous indicator of Ca depletion and cloud physical conditions, and it can vary by factors of more than 30 for adjacent components separated by only several km s<SUP>-1</SUP>; "individual" components derived from lower resolution spectra thus may often be blends of several distinct and physically different parcels of gas.