Along with the other 2 methods mentioned I thought I would add the one that has worked for me. I routinely do deviled eggs for family events (sure makes for a great offering and we always can get them fixed without having to go to the store for special ingredients!
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I thought I'd go nuts the first time I tried peeling fresh eggs, then I tried this method mentioned on a thread here on BYC.
Bring your water to a boil, while it is heating use a straight pin or sewing needle to poke a hole in the rounded end of the egg. You only need to poke it in a very short distance, just through the shell. I simply place them pointy side down back into the egg carton until I have all of them done. Then add them to the boiling water and set your timer to 14 minutes. (I prefer my eggs very hard boiled for my deviled eggs, shorten the time if you are looking for softer boiled eggs)
Once your timer goes off then drain off the hot water, and refill the pot with cold sink water and let it run over till it is reasonably cool. Then simply roll the egg on the counter to break open/loosen the shell and peel. I rarely have a stubborn egg now, even use the eggs laid that day without problem.
Finding that tip on BYC has saved me untold hours of frustration when peeling eggs!