I love cooking with fresh ginger, but rarely do I use the entire root before it dries out in my fridge or cupboard. Freezing ginger will not only make it last for months but you'll also find that it is easier to peel with a standard paring knife and much easier to grate as fresh ginger tends to separate into stringy fibres — grate while frozen to avoid this.
Household weblog The Manly Housekeeper shares that the only disadvantage to freezing ginger is that it is more difficult to cut into chunks when frozen. In that case you may want to peel and slice the ginger before freezing.
Quick Tip: Always Freeze Fresh Ginger [The Manly Housekeeper]