I seem to be using a lot of ginger lately, and have discovered if you tightly wrap fresh ginger in plastic wrap then place it in the freezer.
It will last for much longer, plus be easier to peel and grate.
Garlic is another one that stores well in the freezer. I just break up a bulb of garlic and place it in a Tupperware Antarctica container.
The cloves can then be used as needed, and the papery skin is easily removed.