Devilled duck eggs are the yummiest treat ever. Num!!
Everyone's already hit on the main points, but I wanted to add a few things to try too. The vinegar works great, but even better if you let them soak in it (in the fridge) overnight. About one part vinegar to three parts water should work. It pretty much dissolves all the calcium leaving the eggs with just a thick membrane that peels right off. It's fun to watch too, as it bubbles up and makes the eggs spin in the vinegar. Pretty cool to watch.
Also, if you have really fresh eggs and just can't wait, you can still peel and eat them, it just takes a special knack. First, punch the egg down onto the counter with the air cell down, so you crush the shell right over the air cell (air cell side is the large end). Then firmly roll the egg from air cell end to the other end, so that the shell crumbles starting at the air cell all the way up to the other end. Do this all the way around. Then, roll the whole thing around on the counter a bit to thoroughly crumble the shell. By starting at the air cell end and crumbling it all over, you encourage the shell to separate from the egg, introducing a layer of air all around, and it makes it a little easier to peel. Then you just start peeling (at the air cell end first). I find it works best if I work in a spiral pattern from the top (air cell end), trying to keep the shell attached to the membrane and just gradually working my way down. It's still not perfect, and it's kind of a pain, but once you get the hang of it it's not too bad and it does work a little better.
Now, just think about this. You know how hard it was to peel those eggs. It's because they're fresh. Imagine how old the eggs are that you buy from the grocery store to make them so much easier to peel. Feel better about your backyard-fresh eggs yet? LOL I won't touch store-bought eggs any more. I can't bear to eat them after having lived on our farm fresh eggs for two years.
P.S. When I have excess, I've had good luck selling them. But I also give them away--to friends, business associates, and anyone who needs a little perk-up. I love the feeling I get from being able to help friends and share my bounty.