How to peel hard boiled eggs easily?
Buy almost-late eggs.

The worst-case scenario of egg-shelling is a farm-fresh egg. That annoying film that sticks to both the shell and to the egg will detach, the older the egg gets. The bubble at the fat end, too, will get bigger as the egg ages, which also makes the bottom cap pop off more easily.

Obviously, we don't want rotten eggs. We want the almost expired but not expired ones.
Roll the egg against the countertop, cracking it along the "equator".

This will give you lots of starting points, and it will weaken the shell in enough directions that the rest of the peeling becomes easier. Usually, the top and bottom caps come off in large and clean pieces, so don't bother cracking that part unless it sticks.
Start from the fat end of the egg.

After much experimenting, I've determined that starting from the bottom of the egg (the fat end) is the best way to do it. Give the egg one good whack on the countertop, and the bottom caves in quite easily. This gives you a really nice starting point. Now peel out from there in a spiraling pattern down the rest of the egg. The top cap still comes off quite easily in one big chunk, if the egg is old enough.