(With apologies to author Betty MacDonald.)
I used my mother's method for years: put the eggs in water, bring to a boil, boil for 20 minutes or so, then take out and shock in cold water. The whites were like rubber (I fed mine to the dog) and looked like they'd been pecked by birds because of nicks while peeling and the yolk always had a green circle, but she (and I) didn't know any better. Just as I recently learned a better way to scramble eggs, at some point I learned how to cook a perfect hard-boiled egg like this beauty in the bowl. I think (hope) it's worth sharing.
Part of the problem is in the name. Eggs should never be boiled; it toughens the albumin (the whites) and some chemical reaction creates that green around the yolk. Older eggs are best because they have a larger air sac to expand and allow the shell to separate more easily. Put the eggs in cold water, bring just to a bare simmer, put on a lid and turn off the heat. Let sit 10-15 minutes, drain, and cover with running cold water a short while. They will peel like a dream, the whites will be tender, and the yellow yolks will be cooked all the way through without any discoloration.
I made a bowl of egg salad yesterday for egg-and-ham sandwiches. Nom nom nom.