Place eggs in a saucepan, cover them by an inch or two over the top of the eggs with cold water, and set the pan over high heat. When the water barely reaches a boil (i.e. not yet “rolling”), remove from heat, cover the pan, and let the eggs stand for 12 minutes (note: This is a departure from the article, but to me, 10 minutes sometimes results in runny whites…yuck). Set eggs in an ice water bath, and peel under running water for the easiest shell removal.
As for why sometimes the shell sticks, I am still not sure about that one. One of the great mysteries of life, I guess.
Update (4-16-12): Since writing this post, I have learned that difficulty in peeling can be due to a too-fresh egg. Who knew there was such a thing?
Editor’s note: This post is a part of Monday Mania