I boil them for 5-6 minutes (depending on the heat of your stove burners- less time for gas, five minutes is perfect for my burners, and timing starts once the egg water reaches a boil), then quickly remove them from the heat, dump out the hot water and quickly throw in ice cubes and cold tap water. The reason for timing the five to six minutes is I feel the eggs taste much better when they are JUST cooked, and overcooking them imparts a more sulfur-like flavor and more rubbery texture. They're more tender textured and delicate tasting when they're juuuust done- same principle applies to cooking fish. After around a minute, they can be peeled or stored in the fridge.
My secret to peeling: Usually on one end is an air bubble, usually the wider bottom side. I hit that bubble side against the counter, and then gently administer 2 to 3 more cracks around the rest of the egg so the shells are cracked but not into tiny bits. Start by peeling the shell where the air bubble is...this releases the pressure between the egg shell, that semi transparent membrane and the boiled egg. The rest of the shell will come off very easily with the pressure gone. Also, cooling the eggs right away will keep the shells from really sticking to the egg. Then rinse any remaining bits of shell in the water bath or under a faucet.
Details, details...can you tell I've lived off these things quite a bit???!
I usually eat the whites only and plain, but sometimes I make a dipping sauce out of a mixture of Louisiana Hot Sauce, Soy sauce and Lemon juice.