Fresh eggs are hard - two foolproof methods:
My favorite way: Add 1/3 to 1/2 CUP of salt to the boiling water then, plunge in an ice bath when they're done. Peel when they're cold. It shrinks that inner membrane and they peel like a dream. No, it will not make the eggs salty.
Older eggs peel easier, so if you know you're going to want hard boiled eggs, set however many you want aside in the fridge for about 3 weeks. I'm not this organized, so I always use the salt method.