Conventional wisdom says that if fresh ginger is to remain in a finished dish in any form (grated, minced, chopped, etc.), then it ought to be peeled—some find the peel bitter—whereas if slices are to be thrown in a stock or sauce and removed before serving, they needn’t be peeled.
Chowhounds take varied stances on the ginger-peeling issue. Some don’t bother peeling at all, ever, and just scrub well. Some don’t peel when they can buy fresh, young ginger that has thinner, more tender skin. And some offer tips for making peeling easier, or a nonissue. The easiest way to peel, say several, is using the tip of a spoon, which maneuvers around the knobs more easily than a grater and sacrifices much less flesh than a paring knife. When grating ginger, some find that using a fine Microplane allows the flesh through but keeps the peel back. Some simply store their ginger in the freezer and say they can grate it frozen with none of the peel coming through.
Board Link: Must I Peel the Ginger?