Here is a nice plugin to disable password resets in WordPress: http://wordpress.org/extend/plugins/prevent-password-reset/installation/.

Compared to other plugins this one lets you choose which users are allowed to use the password reset functionality and which are not.  If a user is plagued by password reset emails, just disable it for him.
Another use might be to disable the password reset for the admin user as this user name is commonly known and crackers might try to exploit it.