How to embed YouTube videos in posts without adding suggested videos at the end?

Something like this should do the trick and force rel=0 for all YouTube oembed results.

add_filter('oembed_dataparse','youtube_force_rel',10,3);
function youtube_force_rel($return, $data, $url) {
    if ($data->provider_name == 'YouTube') {
        return str_replace('feature=oembed', 'feature=oembed&rel=0', $return);
    } else {
        return $return;
    }
}