This is probably old news for most people, but hey, it's been over 15 years since I really spent much time cooking and I wasn't ever very good at keeping a kitchen stocked. But, I was flipping through How to Break an Egg to see if there were any good tips that caught my eye, and I started noticing how many left over ingredients you can freeze.
For freezing the ginger, the book recommends peeling it and freezing it directly. You can grate it frozen, and it will thaw almost instantly. I tried grating it before freezing. That might have been a mistake, but we'll see how it goes.
Another tip I got from my neighbor is freezing the juice from left over limes and lemons. Just squeeze them right into an ice tray. One medium lime makes about 3 cubes. Once frozen, pop them out of the tray, and save in a plastic bag. Works great for recipes that call for the juice, or even better in a fresh margarita. I recommend the silicon ice trays if you have them. These are particularly cool: