Since the first successful measurements of stellar trigonometric parallax in the 1830s, the study of nearby stars has focused on the highest proper motion stars (mu > 0.18"/yr). Those high proper motion stars have formed the backbone of the last 150 years of study of the Solar Neighborhood and the composition of the Galaxy. Statistically speaking, though, there is a population of stars that will have low proper motions when their space motions have been projected onto the sky. At the same time, over the last twenty years, populations of relatively young stars (less than ~100 Myr), most of them with low proper motions, have been revealed near (<100 >pc) the Sun. This dissertation is the result of two related projects: A photometric search for nearby (<25 >pc) southern-hemisphere M dwarf stars with low proper motions (mu < 0.18"/yr), and a search for nearby (