There are a few tricks to cooking easy-peeling hard-boiled eggs, but chowhounds note that there’s no guarantee you won’t get a toughie once in a while. As fauchon puts it, “some eggs are just recalcitrant!”
Most important: DON’T use fresh eggs. Age them in the fridge for a couple of weeks before boiling (don’t worry, they’ll be just fine for eating; eggs last a long time uncooked). The whites will evaporate a little, leaving a bit of air between them and the shell when they’re boiled, so you can get the shell off easier.
Once you’ve cooked your eggs, drain off the hot water, fill the pot with ice cubes and cold water, put the lid on, and shake the pot around to crack the eggshells all over. Let the eggs sit in the ice water for 10 minutes or so, then peel under running water.
Board Links: Hard-Boiled Eggs… Getting On My Nerves!