How do I remove the "Request New Password" link? When I visit www.example.com/user, there is a page that shows the login/password and as well as a "Request New Password" tab.

How do I remove this "Request New Password" tab from the user page?
The No Request New Password module is probably the easiest way to go, though you'll need to dig for the 6.x releases. This disables any request to user/password, so this path with neither be accessible directly nor display in menus/tabs/links.

Alternatively, you can put its main function into your own custom module:

 /**
  * Implementation of hook_menu_alter().
  */

 function MYMODULE_menu_alter(&amp;$callback) {  
     $callback['user/password'] = array('access arguments' =&gt; array(FALSE));
 }