Ever had a hard-boiled egg that had a yucky green tinge to the yolk? That's because the egg was overcooked by boiling. Julia Child refers to hard-boiled eggs as hard-cooked, and hers are never boiled. I tried her technique several years ago and they turn out perfectly. The trick is to not actually boil the eggs!
I've read so many of Julia's wonderful books that I can't remember which one this comes from; I think she repeats it in several of them.
GENTLY place 8 raw eggs into a pan and cover with cold water.
Bring to a boil over medium heat. AS SOON AS the water starts boiling, turn the heat off and cover the pan with a tight fitting lid. Let sit, covered for 15 minutes. Drain and rinse with cold water. Let sit until cool enough to handle.
To peel eggs, roll them on the counter top and gently remove shell. Don't worry if eggs don't peel easily; you didn't do anything wrong! Eggshells are easier to remove when the egg is a little older. Hard to remove shells mean the egg is really fresh.
If planning to make deviled eggs, when the eggs have to look good as well as taste good, I look through the egg cartons to find one a little older and buy them a few days ahead of when I need them. No guarantee, but it's worth the shot -- eggs can vary by age even within the same carton. To make sure I have enough that look good, I always make extras. (The ugly ones get used for egg salad!)