A lot of good info, here's my $.02. Soak the broken off bolt/stud with a penetrant such as Kroil or PB blaster and let it soak overnight. If there is enough bolt/stud sticking out to get a pipe wrench on it, use that. If is broken off flush, use a extractor from a company called Greenlee. These extractors are square, not a LH spiral like EZ Outs. In my experience, EZ Outs are poor comparison to the greenlee extractors. If the extractor doesn't work, find the correct tap drill size and drill out the bolt, then use a tap of the correct size to clean the threads out.
I worked with a guy one time, we drilled out a 1 1/2" broken stud and he pulled the threads out with a pair of pliers, it looked like a spring.