Are there any cloud CI services that allow Vagrant VMs to run using VirtualBox as a provider?
Early investigation shows this seems not to be possible with Travis CI or Circle CI, although the vagrant-aws plugin allows for the use of AWS servers as a Vagrant provider. Is this correct?
Many CI services are not allowing to run Vagrant via LXC or Virtualbox as it will require nested virtualization (running VM in VM) or a pure bare metal server provisioned for you.
Current 2021 (updated) situation:
I hope during the time we'll see CI services allowing to run Vagrant with Virtualbox or LXC, but for now Docker (with its limitations) is the only option.
Personally, I would be happy to use it for integration tests against different platforms/linux distros via Test-Kitchen CI or similar.