This code removes all the current default widgets from loading and can be modified to your own needs.

Remove All Default WordPress Widgets

function remove_wordpress_widgets() {
    unregister_widget('WP_Widget_Pages');
    unregister_widget('WP_Widget_Calendar');
    unregister_widget('WP_Widget_Archives');
    unregister_widget('WP_Widget_Meta');
    unregister_widget('WP_Widget_Search');
    unregister_widget('WP_Widget_Text');
    unregister_widget('WP_Widget_Categories');
    unregister_widget('WP_Widget_Recent_Posts');
    unregister_widget('WP_Widget_Recent_Comments');
    unregister_widget('WP_Widget_RSS');
    unregister_widget('WP_Widget_Tag_Cloud');
}
add_action('widgets_init', 'remove_wordpress_widgets', 1);