OpenCPU is the early stages PhD-project of Jeroen Ooms under supervision of Jan de Leeuw at the UCLA. Its buzzwordy tagline "Scientific computing in the cloud" captures it partially, but does not do it justice.
Most notable is that the entire architecture is truly open, not only the software level but also on the API and practical level. I.e. you can download the AGPL-licensed server as a Debian/Ubuntu-package and run your own instance. In addition to that, all interactions with the server take place through a cleanly designed REST-interface and you can execute all standard R-code, including your own.
This level of practical openness is very relevant, as a FOSS-licenced product can still generate a stale software ecosystem around it and practical lock-in due to specific protocols, customized commands, etc.