Plugin that lets visitors Like a post (not facebook) and stores likes in custom meta?

If you still use the plugin WTI Likes you can get the values direkt from the table that the plugin creates instead of saving values to the post meta.

Add this code where you want your list. Now it prints all post that have been liked. From most to least.

<?php

      global $wpdb;

      $query = "SELECT post_id, SUM(value) AS count FROM {$wpdb->prefix}wti_like_post GROUP BY post_id ORDER BY value DESC";
      $posts = $wpdb->get_results( $query );

     if( count( $posts ) > 0 ) {

       foreach ($posts as $post) {
          $post_title = get_the_title( $post->post_id );
          $post_link = get_permalink( $post->post_id );
          $count = $post->count;

          $output .= '<li>';
            // $count shows how many likes the post have
            $output .= '<span>'. $count .'</span>';
            $output .='<a href="'.$post_link.'">'.$post_title.'</a>';
          $output .= '</li>';
        }
      } else {

      $output .= '<li>';
        $output .= __('No posts.', 'mytheme');
      $output .= '</li>';
                }
      echo $output;

?>