WordPress JSON output

If you are using PHP 5.2+ you’re best bet is to just make a PHP array or object and use json_encode().

UPDATED:

$cats = get_categories();
$output = array('categories' => array());

foreach ($cats as $cat) {
    $cat_output = array(
        'cat_id' => $cat->term_id,
        'cat_name' => $cat->name,
        'posts' => array(),
    );

    // should be able to use -1 to get all posts, rather than 9999
    $args = array('numberposts=" => -1, "category' => $cat->cat_ID);
    $myposts = get_posts($args);

    foreach( $myposts as $post ) {
        if ($youtube_id = get_post_meta($post->ID, 'apls_video_youtube', TRUE)) {
            $url = "http://www.youtube.com/watch?v={$youtube_id}";
        } else {
            $url = get_post_meta($post->ID, 'apls_video_hosted', TRUE);
        }

        $cat_output['posts'][] = array(
            'name' => get_the_title($post->ID),
            'url' => $url,
        );
    }

    $output['categories'][] = $cat_output;
}

header("Content-type: application/json");
die(json_encode($output));