Understanding the landscape of potential harms from algorithmic systems enables practitioners to better anticipate consequences of the systems they build. It also supports the prospect of incorporating controls to help minimize harms that emerge from the interplay of technologies and social and cultural dynamics. A growing body of scholarship has identified a wide range of harms across different algorithmic technologies. However, computing research and practitioners lack a high level and synthesized overview of harms from algorithmic systems arising at the micro-, meso-, and macro-levels of society. We present an applied taxonomy of sociotechnical harms to support more systematic surfacing of potential harms in algorithmic systems. Based on a scoping review of computing research ($n=172$), we identified five major themes related to sociotechnical harms - representational, allocative, quality-of-service, interpersonal harms, and social system/societal harms - and sub-themes. We describe these categories and conclude with a discussion of challenges and opportunities for future research.