I learned this trick a couple years ago. For some reason steaming rather than boiling makes the eggs easier to peel. I post it now because I'm about to cook a bunch of eggs for Easter coloring. This works best if you have a steamer basket.
Put about an inch of water in the bottom of a Dutch oven and bring to a boil. Place the steamer basket in the pot, then add as many eggs as will fit (or as you want to cook) in a single layer. Reduce heat to medium-low, cover the pot, and cook for 12 minutes (if using small or very large eggs, you may need to adjust this time up or down).
Remove eggs from heat and cool immediately in ice water unless you want to serve them hot for some reason. Peeling under running water helps keep the job clean by washing away the little bits of shell.
Note: you can make 'soft boiled' eggs this way, too -- just cut the steaming time in half.