Boiled Eggs

Ditto. Cool them immediately after you finish boiling them. Rinse them a couple times in cold water. The egg inside the shell will contract away from the shell when its cooled rapidly, it has more ability to expand and retract than the rigid shell. That makes it easier to peel.

OP If you want to test the freshness of your eggs, break a fresh one and pour it gently into a plate. On a nice fresh egg the yolk will sit up in the white (albumen) and the white will form a nice oval around it. As eggs age the yolk will flatten out and the white will get runnier and will spread more. I was a state FFA poultry judging champion in school and lived in a egg and chicken producing part of the USA for all of my youth.. Funny what sticks in your head.

Older eggs are best (drop in cold water if they sink with a little lean boiled eggs a go go), use cold water after they are ready is a must to shock the parts to seperate. Personally I like to roll them on a hard surface to break the eggshell into a mosaic then peel via the membrane and the shell (usually) sticks to the membrane for an easy clean up. It's all down to eggsperience.

Yep... I have (3) hens and fresh eggs are nearly impossible to peel. I have tried boiling in baking soda and many methods and usually does not help. It is best to 'age' the eggs a few weeks before boiling.

Nothing like getting the egg from the coop and cracking it open for breakfast, though!