With bolts like manifold bolts where they have been heat cycled thousands of times and are generally rusted somewhat, I have found the previously mentioned soaking to be required procedure and heating is a bonus for those with the equipment to do so. In addition I have had good results with actually tightening (even just slightly) the bolts prior to loosening them helps break them loose initially. If they are turning hard while removing it also helps to lube them again and turn them back in rather than trying to keep them coming out.
Exhaust manifold bolts are the most frequently broken ones and require a little extra effort and caution. That usually results in better success and less drilling of broken bolts.