Start full container in Docker?

docker run ubuntu /sbin/init appears to work flawlessly for me with 0.6.6. You won't get a login screen because Docker only manages the process. Instead, you can use docker ps -notrunc to get the full lxc container ID and then use lxc-attach -n <container_id> run bash in that container as root. sshd isn't installed in the container, so you can't ssh to it.

You can use the ubuntu-upstart image:

docker run -t -i ubuntu-upstart:14.04 /sbin/init

Although this solution is unfortunately deprecated, it is good enough if you need a full OS container that 'drives' like a normal Ubuntu 12.04, 14.04 or 14.10 (change the :14.04 bit) system today. If no version is specified it defaults to 14.04. I have not used it heavily, and had some issues installing more complicated packages (e.g. dbus!), but it might work for you.

Alas Ubuntu has switched to systemd in more recent releases. Googling reveals that there seems to be ongoing work to make systemd work in a docker container without requiring elevated privileges, but it does not seem to be quite ready for prime-time. Hopefully it will be ready when 16.04 becomes LTS.

Another option is of course to use phusion/baseimage, but it has it's own approach for starting services. Seems better suited to minimal multi-process containers.