As an attractive business model of cloud computing, outsourcing services usually involve online payment and security issues. The mutual distrust between users and outsourcing service providers may severely impede the wide adoption of cloud computing. Nevertheless, most existing payment solutions only consider a specific type of outsourcing service and rely on a trusted third-party to realize fairness. In this paper, in order to realize secure and fair payment of outsourcing services in general without relying on any third-party, trusted or not, we introduce BCPay, a blockchain based fair payment framework for outsourcing services in cloud computing. We first present the system architecture, specifications and adversary model of BCPay, then describe in detail its design. Our security analysis indicates that BCPay achieves Soundness and what we call Robust Fairness, where the fairness is resilient to eavesdropping and malleability attacks. Furthermore, our performance evaluation shows that BCPay is very efficient in terms of the number of transactions and computation cost. As illustrative applications of BCPay, we further construct a blockchain-based provable data possession scheme in cloud computing and a blockchain-based outsourcing computation protocol in fog computing.