Shave it on top of tofu and eat with tsuyu or soy sauce and some green onion :) Otherwise julienne and put on top of some tender boiled/braised beef. Or cook in sugar water with sweet potatoes and/or taro, or cook in sugar water with silken tofu. Better yet, you can make fabulous chicken pho broth with ginger, onion, and some chicken feet or chicken carcass!

While it doesn't specify young ginger, I made the following for the holidays and it was delicious: http://www.seriouseats...

I've also been making a ton of pho recently and I love it with lots of ginger, or you could make a ginger syryp for drinks, ice cream, etc.

Candied young ginger! http://www.davidlebovitz...

Cut it into cubes, candy it, then use in a vodka martini! trust me, it works.

I'm in love with young ginger! It's so floral and light and blushingly sweet. I infuse it for pot de creme and use the syrup from candying for lemonade... if you candied it and dried/sugared it it might make a gorgeous addition to shortbread... or add it to a quick batch of marmalade. Nice pairings might be rhubarb, quince, grapes, meyer lemons. you are so lucky to find it at a farmer's market!

Shave thin slices of the ginger and place them under the skin of chicken. Then season the chicken with salt, pepper and drizzle lightly with canola or olive oil. Roast the chicken. Serve with soy sauce and scallions.

I used young ginger in this recipe:
http://www.foodnetwork...
It's a great recipe, also very easy, you can see my comments on using the young ginger instead of regular. I am now a big fan, and I plan to add it to other recipes where I like a little extra spike, for example, in my rhubarb-ginger bars muffins, almost anything made with rhubarb or lemon, in jams or chutneys, etc. I think I will use a vegetable peeler or mandoline to slice it really thin, though. I like a little of the chewiness that it has, but I don't want to leave long, tough strings; maybe I will dice it a bit after cutting the thin peels.

Just yesterday, Eugenia Bone had this piece about spring ginger in the NYTimes Dining section...http://www.nytimes.com...

Young ginger is really lovely when pickled (as in the traditional Japanese pickled ginger served with sushi). Thinly slice and pour over it a hot brine made of rice vinegar, sugar, and salt all to taste. I wouldn't can it--just keep it in the fridge.

Just realized you specified "besides pickling it" in your question. Reading is important ;)