I've had good success with a drywall screw and a 1/4" drive socket. Match the socket to just larger than the plug to be removed. Set it in the jaws of a visegrip as a holding device. Set the socket over the plug, pass the screw through the center hole, and into the plug. Screw it down into the plug while applying downward pressure with the socket. As the drywall screw encounters the covered screw head, it will stop and force the plug up and out, while the rim of the socket holds the surrounding surface wood from ripping out.
Try it in stages to ascertain the strength of the glue joint, and behavior of the broken plug as it comes up into the socket. Adjust to taste.
If the plugs are really thin and break out cleanly, you may not even need the socket.
Copied from a SailingAnarchy.com Cruising Forum post by "Panther"