You can wrap fresh ginger in plastic and then seal it in a freezer bag and keep it in the freezer for up to a year. Some people find it a bit soggy as it thaws and object to that, but it retains its flavor, and in many cooked dishes the texture change is not noticeable. You can grate it without thawing, which can save you some time.

You can also store fresh, peeled ginger in a jar of sherry or Madeira for about three months, which will flavor the ginger a bit, but will also flavor the wine and make it particularly suitable for stir-fry dishes, sauces, salad dressings, etc.