I came across this while searching for something else
http://www.urs4.com/technical/repair/stud/stud.html
It details a method for removing studs that are broken off below the surface without drilling. I'd never heard of this method and I thought it might be of interest.
In a nutshell this is the method:
"Using a welder, slowly build up a bead of weld on top of the stud, until it clears the surface of the head. Using vice grips, grab the weld and twist out the stud remains."
-Chris