Copy of the default WordPress category widget - but you can pass a list of IDs to exclude. (Children categories will be excluded as well)

categoryexcluder.php

<?php
/*
Plugin Name: Category Excluder
Plugin URI: https://gist.github.com/1143511
Description: Added a way to pass a list of IDs to be excluded from the default Wordpress Categories widget.
Author: @mertonium
Version: 0.1
Author URI: http://mertonium.com
*/
/**
 * [Custom version of] Categories widget class
 *
 * @since 2.8.0
 */
class WP_Widget_Category_Excluder extends WP_Widget {

  function WP_Widget_Category_Excluder() {
    $widget_ops = array( 'classname' => 'widget_categoryexcluder', 'description' => __( "A list or dropdown of categories" ) );
    $this->WP_Widget('categoryexcluder', __('Category Excluder'), $widget_ops);
  }

  function widget( $args, $instance ) {
    extract( $args );

    $title = apply_filters('widget_title', empty( $instance['title'] ) ? __( 'Category Excluder' ) : $instance['title'], $instance, $this->id_base);
    $c = $instance['count'] ? '1' : '0';
    $h = $instance['hierarchical'] ? '1' : '0';
    $d = $instance['dropdown'] ? '1' : '0';
    $exclude_list = $instance['exclude_list'];

    echo $before_widget;
    if ( $title )
      echo $before_title . $title . $after_title;

    $cat_args = array('orderby' => 'name', 'show_count' => $c, 'hierarchical' => $h, 'exclude_tree' => $exclude_list);

    if ( $d ) {
      $cat_args['show_option_none'] = __('Select Category');
      wp_dropdown_categories(apply_filters('widget_categories_dropdown_args', $cat_args));
?>

<script type='text/javascript'>
/* <![CDATA[ */
  var dropdown = document.getElementById("cat");
  function onCatChange() {
    if ( dropdown.options[dropdown.selectedIndex].value > 0 ) {
      location.href = "<?php echo home_url(); ?>/?cat="+dropdown.options[dropdown.selectedIndex].value;
    }
  }
  dropdown.onchange = onCatChange;
/* ]]> */
</script>

<?php
    } else {
?>
    <ul>
<?php
    $cat_args['title_li'] = '';
    wp_list_categories(apply_filters('widget_categories_args', $cat_args));
?>
    </ul>
<?php
    }

    echo $after_widget;
  }

  function update( $new_instance, $old_instance ) {
    $instance = $old_instance;
    $instance['title'] = strip_tags($new_instance['title']);
    $instance['count'] = !empty($new_instance['count']) ? 1 : 0;
    $instance['hierarchical'] = !empty($new_instance['hierarchical']) ? 1 : 0;
    $instance['dropdown'] = !empty($new_instance['dropdown']) ? 1 : 0;
    $instance['exclude_list'] = strip_tags($new_instance['exclude_list']);

    return $instance;
  }

  function form( $instance ) {
    //Defaults
    $instance = wp_parse_args( (array) $instance, array( 'title' => '') );
    $title = esc_attr( $instance['title'] );
    $count = isset($instance['count']) ? (bool) $instance['count'] :false;
    $hierarchical = isset( $instance['hierarchical'] ) ? (bool) $instance['hierarchical'] : false;
    $dropdown = isset( $instance['dropdown'] ) ? (bool) $instance['dropdown'] : false;
    $exclude_list = esc_attr( $instance['exclude_list'] );
?>
    <p><label for="<?php echo $this->get_field_id('title'); ?>"><?php _e( 'Title:' ); ?></label>
    <input class="widefat" id="<?php echo $this->get_field_id('title'); ?>" name="<?php echo $this->get_field_name('title'); ?>" type="text" value="<?php echo $title; ?>" /></p>

    <p><input type="checkbox" class="checkbox" id="<?php echo $this->get_field_id('dropdown'); ?>" name="<?php echo $this->get_field_name('dropdown'); ?>"<?php checked( $dropdown ); ?> />
    <label for="<?php echo $this->get_field_id('dropdown'); ?>"><?php _e( 'Display as dropdown' ); ?></label><br />

    <input type="checkbox" class="checkbox" id="<?php echo $this->get_field_id('count'); ?>" name="<?php echo $this->get_field_name('count'); ?>"<?php checked( $count ); ?> />
    <label for="<?php echo $this->get_field_id('count'); ?>"><?php _e( 'Show post counts' ); ?></label><br />

    <input type="checkbox" class="checkbox" id="<?php echo $this->get_field_id('hierarchical'); ?>" name="<?php echo $this->get_field_name('hierarchical'); ?>"<?php checked( $hierarchical ); ?> />
    <label for="<?php echo $this->get_field_id('hierarchical'); ?>"><?php _e( 'Show hierarchy' ); ?></label></p>
    
    <input type="text" class="widefat" id="<?php echo $this->get_field_id('exclude_list'); ?>" name="<?php echo $this->get_field_name('exclude_list'); ?>" value="<?php echo $exclude_list; ?>" />
    <label for="<?php echo $this->get_field_id('exclude_list'); ?>"><?php _e( 'Exclude IDs (comma separated)' ); ?></label></p>
<?php
  }

}

add_action('widgets_init', create_function('', 'return register_widget("WP_Widget_Category_Excluder");'));
?>

Setup

• Copy this file into your /wp-content/plugins folder and activate it through the plugins menu.
• It will then appear as an "Available Widget" on your Widgets admin page.
• Enter a comma separated list of category IDs to exclude from the listing.
• Everything else works just like the default WordPress category widget

Note

If an excluded category has sub categories, they will be excluded too.