We present Stampede^RT, middleware designed to provide a natural programming model appropriate for live streaming applications. Such applications require pervasive access to multiple streaming data sources for distributed online analysis. One motivating example is a distributed robotics application which analyzes live camera feeds for control and planning. Most existing middlewares for streaming data focus on media streams and low-level transport characteristics such as delivery latency and efficient transfer, but do not define a programming model to succinctly express applications that manipulate and analyze the streaming content. StampedeRT provides for straightforward transport and manipulation of temporally-ordered data streams, enabling simple synchronization and correlation of data sources. We present an abstract programming model to support the aforementioned class of applications and then describe a concrete realization of the model as a distributed middleware architecture. We also evaluate our implementation of the architecture and present several motivating applications StampedeRT is designed to support.