If you encounter problems after upgrading Wordpress and the AddToAny plugin version .9.9.9.1 (the one I tested), try to update your footer.php file of your current theme too add this line just before the closing body tag: 

<?php wp_footer(); ?>

It seems that newer versions of the plugin put some javascript code into the footer section, so without this call, there's no javascript for AddToAny, and without javascript, you can't see the popup div that allows you to select the service you want to use to share your posts.