This paper describes the e-Science Central (e-SC) cloud data processing system and its application to a number of e-Science projects. e-SC provides both software as a service (SaaS) and platform as a service for scientific data management, analysis and collaboration. It is a portable system and can be deployed on both private (e.g. Eucalyptus) and public clouds (Amazon AWS and Microsoft Windows Azure). The SaaS application allows scientists to upload data, edit and run workflows and share results in the cloud, using only a Web browser. It is underpinned by a scalable cloud platform consisting of a set of components designed to support the needs of scientists. The platform is exposed to developers so that they can easily upload their own analysis services into the system and make these available to other users. A representational state transfer-based application programming interface (API) is also provided so that external applications can leverage the platform's functionality, making it easier to build scalable, secure cloud-based applications. This paper describes the design of e-SC, its API and its use in three different case studies: spectral data visualization, medical data capture and analysis, and chemical property prediction.