That's fairly easy.
You can achieve this using javascript/jquery/server side code etc. Assuming user does click the control.
Something like this on pageLoad
PageLoad()
{
YourDropDownList.Attributes.Add("onclick","javascript:CallHelloWorld();return false;");
}
Then on server side you can decorate a method with WebMethod attribute
[WebMethod()]
public static string HelloWorld()
{
return "Hello foo";
}
On your client side aspx you can use jQuery to call your webmethod
<script language="text/javascript">
function CallHelloWorld()
{
// Call HelloWorld webmethod using jQuery $.ajax
}
</script>
Edit
You can use a radiobutton list instead of dropdownlist. That way, on client side you can check the event when the radio button is clicked that it is checked or not (if its checked fire your event).
Edit
Also try looking at this thread if you want to use dropdown list specificallyFire event each time dropdown list is selected with JQuery