you can remove them by adding a blank text widget
or you can open the sidebar.php file of the theme witch looks like this:
<!-- begin box about -->
<!-- begin sidebar -->
<div id="sidebar">
<h2>About</h2>
<div class="sidebox">
<img id="aboutimg" src="https://wordpress.stackexchange.com/questions/7234/<?php echo get_option("cici_about_image')?>" alt="about" />
<p><?php echo stripslashes(get_option('cici_about_txt')); ?></p>
</div>
<h2>Advertisement</h2>
<div class="sidebox">
<?php if(get_option('cici_ads')=='yes'){?>
<?php include (TEMPLATEPATH . '/ad1.php'); ?>
<?php }?>
<div class="clear"></div>
</div>
<?php if(get_option('cici_videos')=='yes'){?>
<?php include (TEMPLATEPATH . '/video.php'); ?>
<?php }?>
<h2>Popular Articles</h2>
<ul class="popular">
<?php pp_popular_posts(4); ?>
</ul>
<h2>Flickr Photos</h2>
<div id="flickr">
<?php if (function_exists('get_flickrRSS')) get_flickrRSS(); ?>
</div>
<?php
/* Widgetized sidebar */
if ( !function_exists('dynamic_sidebar') || !dynamic_sidebar() ) : ?>
<?php endif; ?>
</div>
<!-- end sidebar -->
</div>
<!-- end colRight -->
and remove all of the static widgets so you get something like this:
<!-- begin box about -->
<!-- begin sidebar -->
<div id="sidebar">
<?php
/* Widgetized sidebar */
if ( !function_exists('dynamic_sidebar') || !dynamic_sidebar() ) : ?>
<?php endif; ?>
</div>
<!-- end sidebar -->
</div>
<!-- end colRight -->
this is right about the Terapathy theme, but you get the point and you can do that to any other theme with static widgets in sidebars.