What is a good way to remove a broken screw in light bulb from it's fixture, when the glass has broken?

Using a potato, place it on the metal rim and unscrew.

King, I heard that using a potato peeled, just shove it up there (the light bulb, silly) and unscrew!!!!

Removing broken light bulbs

Sometimes, especially on exterior light fixtures, the glass bulb breaks away from the metal base. There is no best way to remove the base from the fixture, but here are several options.
Before replacing an exterior light, purchase a higher quality bulb with a better base or a copper base that will not rust. You can also coat the threads of exterior bulbs with a special dielectric grease available at automotive stores. Dry lubricant, Permatex Anti-Seize, and Vaseline will also work.

To remove the broken base, first make sure the power is off. Wear eye protection. Protect the immediate area from broken glass that may remain on the base. I like to use a needle nose pliers to grab the metal rim of the bulb and twist it. You can also jam the nose of the pliers into the base of the bulb to get a grip. Sometimes opening the pliers inside the metal threads will give you a grip.

If all fails, use the needle nose pliers to collapse the metal threads until you can remove them.

Folks have phoned my radio show with the following suggestions for removal:

Use your fingers, protected by heavy gloves (not my idea).
Use a fuse puller the same way I use a needle nose pliers.
Jam into the broken base and turn with:
a large cork.
a wooden ruler.
a wad of white bread (perhaps you need some really heavy Italian bread).
a potato.

(Courtesy : www.misterfix-it.com)

In the UK we use a lot of bayonet-type bulbs. I'm afraid that sometimes the only way if the bulb is really wedged is to cut the power and remove the whole fitting from the cable and use vice & pliers on the bench; tiresome, I know, but sometimes there is no other solution.

Remember: never screw a bulb in overly tightly in the first place! All indoor bulbs should come out with the electricity turned off and two fingernails (or pliers) used.