I always used the step and lift method for chickens, and I use it still now to finish off crippled geese, only I don't take the head off geese like I did on chickens as a kid.

Hold the chicken by the feet and place its head on the ground. Place the instep of your boot on the chickens neck just behind the head so that its head cannot slip between your boot and the ground.... now just give a good lift on the legs and you have chicken in hand, chickens head on the ground. For geese we just pull on the legs until we hear that nice sharp POP! Lights out....

I have taken a birds head off with a load of copper plated 6s. And a friend of mine who hunted a nearby farm a few years ago shot a bird in the fall with a rocket hammerhead and took his head off. I saw the bird immediately following the hunt, but wasn't there for the "kill" myself... don't know if that counts or not.....