Bolt extractors 0.70j

Hello List:
Asking about successful methods listers have used to extract broken bolts 
from various areas. Thinking specifically of broken bolts in the captive 
nuts on various body/fender mounting spots. Is it worth fooling around with 
extractors and the like or is it better to bite the bullet and cut off the 
captive nut/cage and re-install a new one?
Any advice?
Thanks in advance for any hints.
Angelo Graham