I've used screw/bolt extractors in the past with very good results. If it works (never had a case where it did not), then existing threads will not be damaged. No tapping needed, just buy a new bolt in the same size as the old.
You can find bolt extractors in most hardware stores, in all sizes and they are about the cost of a good drill bit (I picked up a kit with about 6 different sizes for about $20). Extractors are simple to use; apply penetrating oil (let it work in real good), drill a hole in the center of the broken bolt, screw in the bolt extractor (correct size to fit in the hole drilled) and use a breaker bar (or wrench with a pipe to extend the handle) to unscrew the broken bolt. The extractor has left hand/reverse threads, so it continues to bite into the broken bolt as you unscrew it.
Chris Glennon - Portland, OR
Last edited by cglennon; 02-16-2009 at 01:19 PM.
Reason: more detail