I have a Macbook Pro partitioned to dual boot Ubuntu or OS X. I've read a couple guides explaining how to run a physical Windows partition as a guest inside VirtualBox. Is the same thing possible with an OS X partition?
yes its possible, i would look at the Ubuntu tutorials, they will most likely also work, with slight variation, in OSx.
VirtualBox will only virtualize OS X Server. Anything else is a violation of the license agreement and that license agreement is honored by VirtualBox, VMware and Parallels.
From the Mac OS X Server EULA:
There's no such clause for the desktop version.
If you want to obey the license there it is. If you want to disregard the license, that's something else.