Knowledge about visualization tasks plays an important role in choosing or building suitable visual representations to pursue them. Yet, tasks are a multi-faceted concept and it is thus not surprising that the many existing task taxonomies and models all describe different aspects of tasks, depending on what these task descriptions aim to capture. This results in a clear need to bring these different aspects together under the common hood of a general design space of visualization tasks, which we propose in this paper. Our design space consists of five design dimensions that characterize the main aspects of tasks and that have so far been distributed across different task descriptions. We exemplify its concrete use by applying our design space in the domain of climate impact research. To this end, we propose interfaces to our design space for different user roles (developers, authors, and end users) that allow users of different levels of expertise to work with it.