This method works great every time.

Easy-to Peel Hard-Boiled Eggs:

Bring enough water to cover the eggs by one inch to a boil in a medium saucepan. Using a ladle, gently lower the desired number of eggs into the boiling water. Cook for 9 minutes for a slightly soft center or 10 minutes for a firmer center. (These times are accurate for up to 20 eggs in one pot.)

Immediately remove the eggs from the boiling water (keep the water boiling) and place in a bath of very cold water under a running faucet for 2 minutes.

Gently lower the eggs back into the boiling waater for 10 seconds. Return the eggs to the cold water bath, gently cracking them, for at least 2 minutes. Keeping the eggs in the cold water bath longer is fine, but will cool the inside of the egg.

The first chilling makes the whites shrink from the shells, while plunging the eggs into the boiling water a second time expands the shell and allows it to pull away from the egg.

Peel the eggs under a stream of cold running water or in the cold water bath.

From 3 Bowls: Vegetarian Recipes from an American
Zen Buddhist, by Seppo Ed Farrey and Myochi
Nancy O'Hara, Houghton Mifflin Company, 2000.