Over recent decades, robotic (or highly automated) searches for supernovae (SNe) have discovered several thousand events, many of them in quite nearby galaxies (distances < 30 Mpc). Most of these SNe, including some of the best-studied events to date, were found before maximum brightness and have associated with them extensive follow-up photometry and spectroscopy. Some of these discoveries are so-called “SN impostors,” thought to be superoutbursts of luminous blue variable stars, although possibly a new, weak class of massive-star explosions. We conducted a Snapshot program with the Hubble Space Telescope (HST) and obtained images of the sites of 31 SNe and four impostors, to acquire late-time photometry through two filters. The primary aim of this project was to reveal the origin of any lingering energy for each event, whether it is the result of radioactive decay or, in some cases, ongoing late-time interaction of the SN shock with preexisting circumstellar matter, or the presence of a light echo. Alternatively, lingering faint light at the SN position may arise from an underlying stellar population (e.g., a host star cluster, companion star, or a chance alignment). The results from this study complement and extend those from Snapshot programs by various investigators in previous HST cycles.