The fresher the egg, the more difficult it is to peel after hard cooking. That's because the air cell, found at the large end of the shell between the shell membranes, increases in size the longer the raw egg is stored. As the contents of the egg contracts, and the air cell enlarges the shell becomes easier to peel. For this reason, older eggs make better candidates for hard cooking. Use eggs that are at least a week old to make peeling easier.

Adding a tablespoon of vinegar to the water will help keep the egg whites from running out of any eggs that happen to crack while cooking, but some people find that the vinegar affects the taste. Adding a half teaspoon of salt to the water as it comes to a boil is also thought to help with both prevention of cracking and making the eggs
easier to peel.

Additional Resources:
http://www.fda.gov/Food/ResourcesForYou/Consumers/ucm077342.htm