Rather than delete this functionality, the best thing to do would be to disable it.
To do this, in your backend go to:
http://YOURSITE.com/index.php?option=com_config&view=component&component=com_users
In the first option which appears, set "Allow User Registration" to No
Once you've done this, you need to create an override in your Joomla template. Simply go to the backend of your site (via FTP) and browse to:
modules/mod_login/tmpl/default.php and copy (be sure not to move it) this file into:
/templates/YOURTEMPLATE/html/mod_login/default.php (If mod_login isn't a folder, just create it).
Once you have got the file in there, open it in your favourite editor and remove the following:
<ul>
<li>
<a href="<?php echo JRoute::_('index.php?option=com_users&view=reset'); ?>">
<?php echo JText::_('MOD_LOGIN_FORGOT_YOUR_PASSWORD'); ?></a>
</li>
<li>
<a href="<?php echo JRoute::_('index.php?option=com_users&view=remind'); ?>">
<?php echo JText::_('MOD_LOGIN_FORGOT_YOUR_USERNAME'); ?></a>
</li>
<?php
$usersConfig = JComponentHelper::getParams('com_users');
if ($usersConfig->get('allowUserRegistration')) : ?>
<li>
<a href="<?php echo JRoute::_('index.php?option=com_users&view=registration'); ?>">
<?php echo JText::_('MOD_LOGIN_REGISTER'); ?></a>
</li>
<?php endif; ?>
</ul>
The above is roughly lines 60 -> 77
That should then revolve it!
Update
If you want to override the user login component, you need to copy the file from
/components/com_users/views/login/tmpl/default_login.php
to
/templates/YOURTEMPLATE/html/com_users/login/default_login.php
and remove this part from the copied file:
<div>
<ul>
<li>
<a href="<?php echo JRoute::_('index.php?option=com_users&view=reset'); ?>">
<?php echo JText::_('COM_USERS_LOGIN_RESET'); ?></a>
</li>
<li>
<a href="<?php echo JRoute::_('index.php?option=com_users&view=remind'); ?>">
<?php echo JText::_('COM_USERS_LOGIN_REMIND'); ?></a>
</li>
<?php
$usersConfig = JComponentHelper::getParams('com_users');
if ($usersConfig->get('allowUserRegistration')) : ?>
<li>
<a href="<?php echo JRoute::_('index.php?option=com_users&view=registration'); ?>">
<?php echo JText::_('COM_USERS_LOGIN_REGISTER'); ?></a>
</li>
<?php endif; ?>
</ul>
</div>
About line 57 ~ 76.
default_login.php
(components/com_users/views/login/tmpl/)