Owing to their utility for measurements of cosmic acceleration, Type Ia supernovae (SNe) are perhaps the best-studied class of SNe, yet the progenitor systems of these explosions largely remain a mystery. A rare subclass of SNe Ia show evidence of strong interaction with their circumstellar medium (CSM), and in particular, a hydrogen-rich CSM; we refer to them as SNe Ia-CSM. In the first systematic search for such systems, we have identified 16 SNe Ia-CSM, and here we present new spectra of 13 of them. Six SNe Ia-CSM have been well-studied previously, three were previously known but are analyzed in-depth for the first time here, and seven are new discoveries from the Palomar Transient Factory. The spectra of all SNe Ia-CSM are dominated by H{alpha} emission (with widths of ~2000 km/s) and exhibit large H{alpha}/H{beta} intensity ratios (perhaps due to collisional excitation of hydrogen via the SN ejecta overtaking slower-moving CSM shells); moreover, they have an almost complete lack of He I emission. They also show possible evidence of dust formation through a decrease in the red wing of H{alpha} 75-100 d past maximum brightness, and nearly all SNe Ia-CSM exhibit strong Na I D absorption from the host galaxy. The absolute magnitudes (uncorrected for host-galaxy extinction) of SNe Ia-CSM are found to be -21.3 <= M_R <= -19 mag, and they also seem to show ultraviolet emission at early times and strong infrared emission at late times (but no detected radio or X-ray emission). Finally, the host galaxies of SNe Ia-CSM are all late-type spirals similar to the Milky Way, or dwarf irregulars like the Large Magellanic Cloud, which implies that these objects come from a relatively young stellar population. This work represents the most detailed analysis of the SN Ia-CSM class to date.
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