Reconfigurable hardware such as FPGAs are being increasingly employed for accelerating compute-intensive applications. While recent advances in technology have increased the capacity of FPGAs, lack of standard models for developing custom accelerators creates issues with scalability and compatibility. We present SHARC - Streaming Hardware Accelerator with Run-time Configurability, for an FPGA-based accelerator. This model is at a lower-level compared to existing stream processing models and provides the hardware designer with a flexible platform for developing custom accelerators. The SHARC model provides a generic interface for each hardware module and a hierarchical structure for parallelism at multiple levels in an accelerator. It also includes a parameterization and hierarchical run-time reconfiguration framework to enable hardware reuse for flexible yet high throughput design. This model is very well suited for compute-intensive applications in areas such as real-time vision and signal processing, where stream processing provides enormous performance benefits. We present a case-study by implementing a bio-inspired Saliency-based visual attention system using the proposed model and demonstrate the benefits of run-time reconfiguration. Experimental results show about 5X speedup over an existing CPU implementation and up to 14X higher Performance-per-Watt over a relevant GPU implementation.