Why isn't wp_enqueue_script('jquery-masonry') working?

jQuery's Masonry is bundled with WordPress. All you should need is wp_enqueue_script('jquery-masonry'); but note that the "slug" is jquery-masonry, not jquery_masonry. And be sure your are enqueueing on the wp_enqueue_scripts hook or later.

function enqueue_masonry() {
  wp_enqueue_script('jquery-masonry');
}
add_action('wp_enqueue_scripts','enqueue_masonry');

I'd guess that your problem has something to do with when you register/enqueue because loading core scripts is pretty straightforward.

If that doesn't work, something is wrong with your site. A plugin or a theme is deregistering, perhaps. Without more information it is going to be hard to say what.

s_ha_dum is correct, you don't need to enqueue it yourself.

That being said, the reason your script is not working is because your dependancy variable is not an array. Your code should read:

wp_register_script('jquery_masonry', includes_url(). '/js/jquery/jquery.masonry.min.js', array( 'jquery' ) );

Way down deep in the WP_Dependancies class, if the value passes is not an array, it sets it to be a blank array, therefore making it have no dependancies. (see wp_includes/class.wp_dependancies.php line 251 as of WP 3.6, if interested)

So what I assume is happening, is it's loading in the Masonry script BEFORE jQuery is loaded in, therefore causing it to do nothing.

That being said, use s_ha_dum's response, as it's already registered in WordPress, and waiting to be en-queued.