This tutorial will show you how to use jQuery to allow as list (UL) to be reordered and will also make an AJAX call to a PHP file that will update the database when an item is dropped. I found this useful for a project I was working on recently. The user wanted to be able to change the order that categories displayed in a report. The items are stored in a database with a field called display_order. When the report is generated we simply order by that field.
This tutorial will walk you through checking for an e-mail to be valid as the user is filling out the form without having to reload the page.