Broke my water pump bolt. Now what? (Update - broken bolt is out)

Several say here to heat the bolt. I say no. You heat the surrounding area, to expand the locking threads. Most of the time the reason a bolt breaks here is because the shoulder of the bolt is locked into corrosion from the pump or timing cover. I agree with the other options of removal but would like to add one more, if other ways do not work. Set a spacer on you drill bit to go as deep as the pump or cover, less 3/8 of an inch. That should remove the area of the corroded parts. Then you should be able to use vice grips to remove the rest of the bolt from the block. I always use a anti-seize in this application on the shoulder of the bolts.
Yeah I agree with your reasoning for why a bolt would break there. But since he got the rest of the bolts out and the water pump off, I still say it probably won't take much to get the stub out, since the aluminum, and the rest of the bolt is already gone... and the corrosion didn't seem to run down the bolt threads into the cast iron..... it's gonna be tough to heat the bolt without heating the cast iron around it if using a torch. If he had just a little more stick out id say to try and induction heater like a "bolt buster" (I actually have the competition model, the "mini doctor" at home) to heat the stub without heating the cast iron as much. I'm not sure there's enough sticking out for that to work though.