This is now provided by Microsoft for free for teams of up to 5 people by Team Foundation Server.
It provides:
- Source Control: TFS, Git
- Agile Planning: Agile, Scrum, CMMI
- Continuous Builds
- Collaboration
- Integration
- Test Execution
- Deployment
Visual Studio Team Services doesn't require hosting code on it, code can be pulled from GitHub or any Git repository.
If the project is small and doesn't have complex requirements to build, Hosted pool can be used to perform CI builds. There're several limitations: available software, one build at a time, time limit of one hour etc. If it isn't enough, you can add your own build agents by running a script on your machines.
GitHub support isn't full (pull requests aren't built, for example), but most functionality is supported. Shields.io doesn't support VSO yet, but a custom shield is available.
The primary drawback for open-source projects is that build logs, test results and other data won't be public. Only five users can be given access to the project on a free account. There's a suggestion on UserVoice to make public projects possible.