This tutorial does more than disable the subject. It removes it completely.
First you want to open you comment.tpl.php file which can be found in drupal directory (on your server) / themes / current theme / comment.tpl.php
Open that file. You will see a code that looks like the following:
<div class="comment<?php print ($comment->new) ? ' comment-new' : ''; print ($comment->status == COMMENT_NOT_PUBLISHED) ? ' comment-unpublished' : ''; print ' '. $zebra; ?>">
<div class="clear-block">
<?php if ($submitted): ?>
<span class="submitted"><?php print t('!date — !username', array('!username' => theme('username', $comment), '!date' => format_date($comment->timestamp))); ?></span>
<?php endif; ?>
<?php if ($comment->new) : ?>
<a id="new"></a>
<span class="new"><?php print drupal_ucfirst($new) ?></span>
<?php endif; ?>
<?php print $picture ?>
<h3><?php print $title ?></h3>
<div class="content">
<?php print $content ?>
</div>
</div>
<?php if ($links): ?>
<div class="links"><?php print $links ?></div>
<?php endif; ?>
</div>
Inside that code locate a smaller code that looks like the following:
<h3><?php print $title ?></h3>
Delete that small code.
*SAVE AND CLOSE ALL FILES*
Done. Now you have a site that has subject-free comments.