I just finished adding a new privacy setting allowing members to disable the password reminder feature on their account. It also disables the Username reminder feature as well.
The setting should only be used if there is no chance it will be needed in the future, since not even the member will be able to obtain a password reminder once the setting is enabled.
The password/Username reminders are on the Log In page, but those who are certain that they will never forget their password might as well turn it off, since it closes a potential security risk. (There would only be a security risk if somebody has access to your e-mail box, and could view a password reminder that they have e-mailed to you.)
The setting to turn off password reminders is located in the E-mail Settings page (Control Panel menu).
Thanks to Lucky for the inspiration for this idea.