Add / Remove classes from the body_class or post_class

body_class.php

<?php

function wpse15850_body_class( $wp_classes, $extra_classes )
{
    // List of the only WP generated classes allowed
    $whitelist = array( 'home', 'blog', 'archive', 'single', 'category', 'tag', 'error404', 'logged-in', 'admin-bar' );

    // List of the only WP generated classes that are not allowed
    $blacklist = array( 'home', 'blog', 'archive', 'single', 'category', 'tag', 'error404', 'logged-in', 'admin-bar' );

    // Filter the body classes
    // Whitelist result: (comment if you want to whitelist classes)
    $wp_classes = array_intersect( $wp_classes, $whitelist );
    
    // Blacklist result: (uncomment if you want to blacklist classes)
    // $wp_classes = array_diff( $wp_classes, $blacklist );

    // Add the extra classes back untouched
    return array_merge( $wp_classes, (array) $extra_classes );
}
add_filter( 'body_class', 'wpse15850_body_class', 10, 2 );