Great topic. Soups are great, and really anything fresh is where they shine I think. Freezing, drying doesnt do much for me. I use them for interplanting to protect certain plants. You could try selling them around your area, if people like that sort of thing in your area. Have you ever tried the bulbs underground? Im sure they would taste like garlic/onion.
I just recently obtained some garlic chive plants. I used to grow them years ago and cooked them in stir-fry. They are used a lot in oriental cooking. Google "garlic chive recipes" and you will find lots of suggestions.
Chive pesto: 2 cloves garlic 3 tbsp basil 1 cup chives ( I also use spring garlic stems) 1 med onion 1/3 cup pine nuts (I'm near filbert country so I have used them as well as almonds and pumpkin seeds for a substitute) Olive oil usually a little over 2 tbsp.
I occasionally use the pesto when kneading up a loaf of bread
Our inability to change everything should not stop us from changing what we can.
Asian cultures make a lot more use of them than we do. There is a large gourmet and specialty produce market near me that carries a tremendous selection of Asian items. They have several kinds of garlic chives, some with wider blades and others with thinner blades. They also carry a kind that has been blanched (could be done at home under a black plastic pot most likely) that is pale yellow. The length of the bunches is usually impressive, generally around a foot long. The bunches are quite large, much larger than a traditional "bunch" of herbs one would find at a grocery store -- generally about 3 to 4 inches in diameter at the point they are bunched. These are used not just in small amounts as an herb/seasoning, but are actually used in bulk, generally stir-fried, as a vegetable.
I don't really like the flavor of green onions (plus now that I grow them I can't stand the thought of pulling an onion before it bulbs!). So we use the garlic chives for any and all recipes that call for them unless it's the dead of winter and we have the walking onions growing as those are good too!
A few people mentioned asian cuisine. Chinese especially uses them, like in dim sum, with shrimp. There is even a chinese green onion "cake" that would probably taste good with chives subbed for green onion.
I don't know what a home cook would use this idea for, but in a restaurant i worked, we would blanch chives or garlic chives, more like a quick flash in hot water, and use as "string" to tie up things, like a bundle of asparagus or a mini bouquet of fresh herbs.