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Using needle nosed pliers, it is usually possible to bend the lamp base slightly, then turn the base in the socket.
A large eraser will work, so will a piece of crushed newspaper or a chunk of dry sponge.
Use your imagination. On occasion, when there was no broken glass I have even just pressed two fingers against the lamp base and turned it out that way. But be careful that your fingers don't slip, or you might cut them.
And when replacing the bulb - spray a bit of WD40 on the new bulb base, or smear a bit of dielectric grease on it - doesn't take much. Will prevent corrosion next time.
I wouldn't use WD40, as it is flammable. But a TINY amount of petroleum jelly has worked fine for me in outdoor fixtures. I have never had a problem indoors.