I've been freezing shredded zucchini for years with great success. I shred, drain and store in ziplock bags. Usually double-bag.
When I'm ready to use the zucchini and, as someone already said, I drain it. I've discovered that it produces a far superior zucchini bread than freshly-shredded zucchini does. Not sure why. Use it in pancakes, too. Really delicious. You can add it to meatloaf to extend the meat mixture and add moisture. Good way to get children to eat their vegetables without knowing it.
I also "chunk" it for use in soups, etc. Great veggie.