This may be the quickest quicktip we've ever written - if your site doesn't require the "Request new password" functionality, the No Request New Password module makes it pretty easy to remove it. 

Before:

No Request New Password screenshot - before

After:

No Request New Password screenshot - after

Also - the module doesn't just hide the "Request new password" link, it removes the functionality completely, so if a user navigates directly to /user/password, they'll be redirected back to the login page.