Safe Ways to Remove a Light Bulb that Broke Off at the Base
Begin by Turning Off the Circuit Breaker to the Light
It takes more than just turning off the light switch to insure safety when removing a light bulb that broke away from the base. Turn the electricity off at the source. Flip the circuit breaker to the off position, and make sure that the correct panel switch is in fact off. When in doubt, flip the main switch. You will have to reset clocks and other electrical items, but it is the safest solution to a common problem.
Use Duct Tape to Remove the Bulb
Duct tape has been deemed a miracle product. It is sturdy, very sticky and many people say that if something cannot be repaired with duct tape, it is beyond repair. When a light bulb breaks away at the base, duct tape can be used to twist it away safely and easily. Cut off a long piece of duct tape, and wad it up into a ball. Push a portion of the big wad of tape firmly into the base. Use it to safely turn the base and remove it.
Needle Nose Pliers Can Be Used
Do not be afraid to use metal tools to remove a light bulb that broke off at the base. As long as the electricity is not on, it can be accomplished safely and easily. Needle nose pliers can be used, and they will work better than any other metal tool. Simply open up the piers within the base, and remove the piece by turning it from the inside. Once enough of the metal is exposed, a gloved hand can be used to remove it as usual.
Source: Ask Heloise Column, The Times of Northwest Indiana, January 12, 2013 Edition