This tip is has been in my family for years. Has a light bulb ever broken in when it was being screwed in? If so, a good way to get it out after is to use a potato.
Get a potato (preferably around the size of the light bulb opening). Turn off the light. Then, push the potato into the broken end. Twist it in, and then reverse your twisting to unscrew it out. Your problem is now fixed.
