How to remove the word "New" for the new comments When I add a new comment, the word &quot;New&quot; is printed at the top:

I don't need it. This word can be removed by editing the file /modules/comment/comment.tpl.php:
//remove these 3 lines, and the word will disappear
&lt;?php if ($new): ?&gt;
  &lt;span class=&quot;new&quot;&gt;&lt;?php print $new ?&gt;&lt;/span&gt;
&lt;?php endif; ?&gt;

But I don't think, that changing core modules is a good idea.
How can I remove the word without changing the core files?
copy /modules/comment/comment.tpl.php to your theme folder e.g. sites/all/themes/mytheme/(templates/)comment.tpl.php.

That theme file will override the comment.tpl.php from core, in that file you can remove this block:

&lt;?php if ($new): ?&gt;
  &lt;span class="new"&gt;&lt;?php print $new ?&gt;&lt;/span&gt;
&lt;?php endif; ?&gt;


This way is perfectly fine, you are not changing/ hacking core. The theme system was meant to be used that way :)