To boil eggs without cracking them, cover the eggs in a pot with cold water and heat on high to a roiling boil. Boil for one minute, remove from heat and allow them to sit in the water for 12-15 minutes, according to Russ Parsons of the LA Times.
Allowing the cooked eggs to stand in the hot water for 12 minutes will leave the yolks a "golden orange," while 15 minutes will produce a "moist yellow," as explained by Parsons. It's important to start with cold water, as this will reduce the chance of the eggs breaking during boiling.
Elise Bauer of SimplyRecipes.com recommends turning off the heat after the water reaches a full boil and leaving the eggs covered on the hot burner for 10-12 minutes before draining the water. Those who prefer firmer yolks may leave the eggs up to 18 minutes with fear of overcooking. She also suggests that adding a teaspoon of vinegar to the water before cooking may help reduce the chance of egg white escaping if the shell does crack. Adding a half teaspoon of salt may help prevent cracking as well. People living at high altitudes may have to boil eggs longer for the same results.