Please note that this article only applies to Mojang accounts. For older Minecraft accounts that have not been migrated (you log in with your username), please visit this article.
To change the email on a Mojang account, visit account.mojang.com/me/settings. You can either have instructions sent to your current address, or if you don't have access to that email, you can have it changed by passing a security challenge.
If you have registered for a Mojang account using the incorrect email, and have not made a purchase, you can just re-register under the correct address.
If you are unable to change your email, please locate your order number, transaction ID or gift code and contact customer support.