From Learn2.com, in their tutorial on hard-boiling eggs:
Immediately soak the eggs in cold water. This will stop the eggs from cooking by their own heat, and will also help with peeling them. Keep them in the cold water for 30 seconds or so, or until you can handle them without shouting "Ow, ow, ouch!!" and passing them hurriedly from hand to hand. While they're in the cold water, a layer of steam develops between the shell and the egg white. The steam makes peeling an egg much easier.
Additional comments from The Joy of Cooking:
Much discussion swirls around the best way to peel a hard-boiled egg. Very fresh eggs (less than 3 days old) are the most difficult to peel. The older an egg, the larger the air cell, and the neater it peels. Thoroughly chilling hard-boiled eggs before peeling helps by firming the white. Holding an egg under a stream of water as you peel removes any bits of broken shell.
Some cooks advocate a two-step method that involves plunging the cooked egg into ice water for two minutes, then reboiling it for exactly 30 seconds and peeling it immediately.
The Joy of Cooking also comments that eggs should not actually be boiled; they should be put in simmering water and cooked gently. Higher heat overcooks the proteins, leaving the egg white tough and rubbery. Overcooking may also cause a greenish black rim to form between the yolk and the white. This is harmless but yucky when it comes to gourmet cooking.
We looked in several cookbooks, all of which said that when you take the eggs off the heat, you plunge them immediately in cold water to halt the cooking, as well as to help with the peeling.