The increase of mobile and interconnected devices demands for equally ubiquitous and mobile applications. Due to the heterogeneity of devices, applications have to adapt themselves to the environment they are executed in. This requires context management in the environment and context-sensitivity of the application. In this paper, we present a generic context service with a novel generic context model. Our context service has a modular architecture and provides context collection, discovery and monitoring. It offers extension points for integrating future context domains and provides a Web service interface for standard-compliant interaction in heterogeneous environments. We sketch the integration of the prototype into our SAMProc middleware, which provides adaptivity as well as migratability to applications. As a use case, we outline a novel context-aware mobile media player application, which uses context for automatically migrating in order to follow the mobile user and for selecting the best presentation device in the user's surroundings.