ASP.Net MVC - How to postback to the server when a dropdown changes

I recently needed to call a controller action on the server when a dropdown list on a web page changed. This is a fairly common scenario and in this case I was needing to show a list of options from the database based on the value of the dropdown. If the dropdown was contained within a form element I could have called the form submit method and posted back that way, but it wasn't so I had to come up with another way.