Disable register email notification
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.