Moving objects (e.g., vehicles in road networks) continuously generate large amounts of spatio-temporal information in the form of data streams. Efficient management of such streams is a challenging goal due to the highly dynamic nature of the data and the need for fast, on-line computations. In this paper we present a novel approach for approximate query processing about the present, past, or the future in spatio-temporal databases. In particular, we first propose an incrementally updateable, multi-dimensional histogram for present-time queries. Second, we develop a general architecture for maintaining and querying historical data. Third, we implement a stochastic approach for predicting the results of queries that refer to the future. Finally, we experimentally prove the effectiveness and efficiency of our techniques using a realistic simulation.