It has been found that He-3 under pressures of a few atmospheres dissolves in the solid polymers Lucite, Nylon, Delrin, polyethylene, Teflon, and Lexan sufficiently to yield strong helium NMR spectra. The peaks range from sharp (Lucite, Lexan) to relatively broad (nylon, Delrin). The signals are interpreted as indicating rapid motion among sites. Helium NMR signals were also seen in the organic polycrystalline solids benzene, durene, naphthalene, phenanthrene, tert-butyl alcohol, acetic acid, and hexamethylbenzene. More complicated spectra with broader lines were obtained. Changes on repeated melting and refreezing are interpreted to indicate shift dependence on the orientation of individual crystallites. It is considered that He-3 NMR spectroscopy is likely to yield valuable information about sites available and motion among them in a variety of solids in the future.