Removing default theme widgets

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.