If you have registered a Mojang account and would like to delete your account, please visit your account settings page. Please be aware that if your account is deleted, you will no longer be able to log into Mojang services, and will not be able to purchase future Mojang games.
Old Minecraft accounts (those that log into Minecraft with their username) do not have a deletion feature, and no not track account changes like Mojang accounts, therefore deletion is not offered for that account type. If you wish to delete an old Minecraft account, you first need to migrate it into a Mojang account.
If you for some reason are unable to delete the account yourself you can contact customer support. If you have made a purchase on your account, your transaction ID is required.