Are your eggs super fresh? They tend to be harder to peel if they are. Here's a recent thread with a link to others, with probably more opinions and info that you ever wanted to know. Again, welcome! Look around the various forums and join on in!
Since you asked...I had the same problem. I bought a $15 gizmo at Walmart that holds 6 eggs and steams the eggs hard boiled. You pierce the top of the egg, then steam them. When done, you plunge them into cold water. The sudden cooling sucks water into the egg shell from the hole. They peel really easy after that. My wife and I had egg salad sandwiches for a long time. Best thing I ever got.
Yes I can vouch for the easier peeling resulting from making a hole in the wider end of the egg first (that has the air). Also I tend to very lightly 'bash' the egg (once done) and roll it a little. The rolling helps keep the pieces together when peeling.
__________________ "All you need is love. But a little chocolate now and then doesn't hurt" (Charles M. Shulz)
I've tried various foolproof methods for peeling eggs and I still run into an egg from time to time that just does not peel easily or perfectly. If I am making deviled eggs and need pretty eggs I cook one or two more than I need, if I find a clunker in the batch I chop it up and add it to the filling, no worries!
I pierce the blunt end of each egg with a push pin and cook it to hard boiled.
Then I pour off the hot water, shake the pan with the eggs to crack the shells all over and fill the pan with ice water. When the eggs are completely cooled, I peel then under a trickle of cold tap water.
As someone else mentioned, older eggs are easier to peel. So if you're getting eggs ready for Easter, go out and buy them today.
I hesitated to post here as I fear another 100+ post thread on hard boiled eggs. We already have several.
"If you want to make an apple pie from scratch, you must first create the universe." -Carl Sagan