Disable register email notification I have made a deep research over the web and I also tried a lot of alternative solutions, but I didn't find any solution to disable the email notification for new users. 

In my User Settings, I have the option "Visitors can create accounts but administrator approval is required" checked, and the option "Require e-mail verification when a visitor creates an account" not checked.

Do you have any idea?
If you look at the function _user_email_notify(), it checks the variable 'user_mail_' . $op . '_notify' if it should send an email or not. Assuming that you have disabled email confirmation (otherwise, disabling mail notifications would be weird ;)), the $op is 'register_no_approval_required'. So the full variable name is 'user_mail_register_no_approval_required_notify'.

There doesn't seem to be a User Interface for that variable. However, you can set it in your settings.php, adding the following line at the end of settings.php (probably inside sites/default).

$conf['user_mail_register_no_approval_required_notify'] = FALSE;


You can do the same for other mail notifications too; the other possible $op values are listed on the linked page.