So's WordPress Featured Categories Widget: displays a customized list of featured categories

so-featured-categories-widget.php

<?php

/**
* Description: So's WordPress Featured Categories Widget: displays a customized list of featured categories
* Author: Ulrich SOSSOU
* Author URI: http://ulrichsossou.com/
* Version: 1.0
* Licence: GPLv2
* Compatibility: WordPress 3.0+
*
*/

/*
Copyright (C) 2010 Ulrich SOSSOU

This program is free software; you can redistribute it and/or
modify it under the terms of the GNU General Public License
as published by the Free Software Foundation; either version 2
of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/

class SO_Widget_Featured_Categories extends WP_Widget {

	function SO_Widget_Featured_Categories() {
		$widget_ops = array('classname' => 'widget_featured_categories', 'description' => __( 'A customizable list of featured categories', 'so' ));
		$this->WP_Widget('so-featured-categories', __( 'Featured Categories', 'so' ), $widget_ops);
	}

	function widget( $args, $instance ) {
		extract($args);
		$title = apply_filters( 'widget_title', empty($instance['title']) ? '' : $instance['title'], $instance, $this->id_base);
		$categories = explode( ',', empty($instance['categories']) ? '' : $instance['categories'] );
		foreach( $categories as $key => $value ) {
			$categories[$key] = trim( $value );
		}
		echo $before_widget;
		if ( !empty( $title ) ) { echo $before_title . $title . $after_title; } ?>
			<ul class="so-featured-categories">
			<?php
			foreach( $categories as $category ) {
				$category = get_category_by_slug($category);
				if( $category ) {
					$rand_post = new WP_Query( array( 'posts_per_page' => 1, 'orderby' => 'rand', 'cat' => $category->term_id ) );
					$rand_post = $rand_post->get_posts();
					$rand_post = $rand_post[0];
					echo '<li>
							<span class="cat-thumb">' . get_the_post_thumbnail( $rand_post->ID ) . '</span>
							<span class="cat-title"><a href="">' . $category->name . '</a></span>
							<span class="cat-desc">' . $category->description . '</span>
							<span class="cat-count">' . __( 'Posts', 'so' ) . ': ' . $category->count . '</span>
						</li>';
				}
			}
			?>
			</ul>
		<?php
		echo $after_widget;
	}

	function update( $new_instance, $old_instance ) {
		$instance = $old_instance;
		$instance['title'] = strip_tags($new_instance['title']);
		$instance['categories'] = strip_tags($new_instance['categories']);
		return $instance;
	}

	function form( $instance ) {
		$instance = wp_parse_args( (array) $instance, array( 'title' => '', 'categories' => 'uncategorized, featured' ) );
		$title = strip_tags($instance['title']);
		$categories = strip_tags($instance['categories']);
?>
		<p><label for="<?php echo $this->get_field_id('title'); ?>"><?php _e( 'Title:', 'so' ); ?></label>
		<input class="widefat" id="<?php echo $this->get_field_id('title'); ?>" name="<?php echo $this->get_field_name('title'); ?>" type="text" value="<?php echo esc_attr($title); ?>" /></p>

		<p><label for="<?php echo $this->get_field_id('categories'); ?>"><?php _e( 'Categories (enter a comma-separated list of categories slugs):', 'so' ); ?></label>
		<input class="widefat" id="<?php echo $this->get_field_id('categories'); ?>" name="<?php echo $this->get_field_name('categories'); ?>" type="text" value="<?php echo esc_attr($categories); ?>" /></p>
<?php
	}
}

It should work fine with the latest version of WordPress.