"B Moody" wroteclip) Stick a wooden dowel, 8-10" long in the hole and
tap. The bit should pop out of the other end. I use a wooden dowel
because I would be afraid of damage otherwise.(clip)
^^^^^^^^^^^^^^^
Sometimes those can be VERY hard to dislodge, so don't be too surprised if
the wooden dowel doesn't do it. BE CAREFUL not to crush the dowel in there
so you can't get it all out. If the dowel just mushrooms, or splits, or
just bows, and doesn't do it, don't hesitate to use a metal drift. It
should be as large a diameter as will fit in, to minimize bowing. Use a
good heavy hammer, but start with sharp, light blows, and keep increasing
the blows. If you do damage the small end of the taper, that's not the end
of the world--you need it out of there. If you do spread the end a little,
you can dress it on a grinding wheel and still use it.

Sometimes it helps to apply heat, but that's a whole 'nother story.