With a really dumb move, I removed the pulseaudio package on my machine and reinstalled it. The resulting desktop is broken (all the packages that are dependent on pulseaudio have not been reinstalled) i.e. I have no sound :-)
Is there a package whose dependencies can restore a working system? I was thinking of maybe the desktop (unity), or in a ideal world a meta package for the whole distro. Or am I looking at a complete reinstall from a live-CD?