<?php
function mytheme_body_class($classes) {
    global $post;

    if (is_single()) {
        $categories = get_the_category($post->ID);

        if (isset($categories) && is_array($categories)) {
            foreach ($categories as $category) {
                $classes[] = $category->slug;
            }
        }
    }

    return $classes;
}
add_filter('body_class', 'mytheme_body_class');
?>