Recent work on querying data streams has focused on systems where newly arriving data is processed and continuously streamed to the user in real time. In many emerging applications, however, ad hoc queries and/or intermittent connectivity also require the processing of data that arrives prior to query submission or during a period of disconnection. For such applications, we have developed PSoup, a system that combines the processing of ad hoc and continuous queries by treating data and queries symmetrically, allowing new queries to be applied to old data and new data to be applied to old queries. PSoup also supports intermittent connectivity by separating the computation of query results from the delivery of those results. PSoup builds on adaptive query-processing techniques developed in the Telegraph project at UC Berkeley. In this paper, we describe PSoup and present experiments that demonstrate the effectiveness of our approach.