Emerging accelerating architectures, such as GPUs, have proved successful in providing significant performance gains to various application domains. This is done by exploiting data parallelism in existing algorithms. However, programming in a data-parallel fashion imposes extra burdens to programmers, who are used to writing sequential programs. New programming models and frameworks are needed to reach a balance between programmability, portability and performance. We start from stream processing domain and propose GStream, a general-purpose, scalable data streaming framework on GPUs. The contributions of GStream are as follows: (1) We provide powerful, yet concise language abstractions suitable to describe conventional algorithms as streaming problems. (2) We project these abstractions onto GPUs to fully exploit their inherent massive data-parallelism. (3) We demonstrate the viability of streaming on accelerators. Experiments show that the proposed framework provides flexibility, programmability and performance gains for various benchmarks from a collection of domains, including but not limited to data streaming, data parallel problems, numerical codes and text search. This work lays a foundation to our future work to develop more general data parallel programming models for many-core architectures.