Scattered-light echoes from variable and cataclysmic stars offer one of the most effective means to probe the structure and composition of circumstellar and interstellar media. I build a simple model of light-echo surface brightness by considering the source spectrum and the dust density, geometry, and scattering efficiency. I use this model to investigate whether echoes should be observable around short and long-period giants, cataclysmic variables, and supernovae. Only supernovae are expected to illuminate material on both circumstellar and interstellar scales. Giant and post-AGB stars (e.g., Cepheids and Miras) with high mass-loss rates can produce observable echoes within their circumstellar envelopes. Echoes from novae and dwarf novae are probably detectable only from nearby material, and only in unusually dense gas. I present characteristic exposure times to image such echoes over a wide range of wavelengths for ground-based and Hubble Space Telescope observations. I apply these results to analyze the dust properties of the recently reported echoes around SN 1993J, finding the dust in M81 to have a grain-size distribution and chemical composition consistent with Galactic dust. Optimal observing strategies for echo detection are also discussed.