Place this code in your function.php file
If you want to leave a widget just delete the string with its name
function remove_default_widget() {
unregister_widget('WP_Widget_Archives'); // Archive widget
unregister_widget('WP_Widget_Calendar'); // Calendar widget
unregister_widget('WP_Widget_Categories'); // Categories widget
unregister_widget('WP_Widget_Meta'); // Meta widget
unregister_widget('WP_Widget_Pages'); // Pages widget
unregister_widget('WP_Widget_Recent_Comments'); // Latest comments
unregister_widget('WP_Widget_Recent_Posts'); // Latest Post
unregister_widget('WP_Widget_RSS'); // RSS widget
unregister_widget('WP_Widget_Search'); // Search widget
unregister_widget('WP_Widget_Tag_Cloud'); // Tag widget
unregister_widget('WP_Widget_Text'); // Custom text widget
unregister_widget('WP_Nav_Menu_Widget'); // Menu widget
}
add_action( 'widgets_init', 'remove_default_widget', 20 );