The conscientious cook seeking to prepare the perfect hard-boiled egg encounters two problems: an unattractive green ring around the yolk and difficulty of peeling the shell. We shall tackle these problems one at a time.
The Nasty Green Ring: Where It Comes From
Eggs are more than protein and fat: they contain minerals as well, specifically sulfur in the white (albumen) and iron in the yolk. When an egg is boiled for a length of time, these elements combine to produce an unattractive green ring around the yolk. The solution is to cook the eggs just long enough for the yolks to set up, but not so long as to produce an undesirable chemical reaction.
Aack! The Shell Is Sticking To The Egg
For ease of peeling, cooking authorities recommend using eggs 7 to 10 days old. Older eggs have a different pH from fresh eggs, which apparently affects how the shell clings to the cooked white. However, if you are planning a party, you may not have the foresight (I don't) to purchase eggs for hard boiling a week in advance. If older eggs are not available, hard-boiled eggs are made easier to peel by plunging them into an ice-water bath immediately after cooking.
Kill Two Birds With One Stone
Place your eggs into a pot of cold salted water and bring to a boil. Remove the eggs from the heat and let stand for a minimum of 13 minutes, but no more than 20 minutes. Drain the water and place the eggs into an ice water bath until they are completely cool. Refrigerate the eggs if you are not going to use them immediately.
Sources: FoodTV.com and MarthaStewart.com