We consider the problem of approximating sliding window joins over data streams in a data stream processing system with limited resources. In our model, we deal with resource constraints by shedding load in the form of dropping tuples from the data streams. We first discuss alternate architectural models for data stream join processing, and we survey suitable measures for the quality of an approximation of a set-valued query result. We then consider the number of generated result tuples as the quality measure, and we give optimal offline and fast online algorithms for it. In a thorough experimental study with synthetic and real data we show the efficacy of our solutions. For applications with demand for exact results we introduce a new Archive-metric which captures the amount of work needed to complete the join in case the streams are archived for later processing.