Implement a custom ASP.NET ListControl that post back data with javascript
$.ajax({
         type: "GET",
         url: "process_me.aspx?value=" + $("#id-of-hidden-value-of-list").val(),
         success: function(){
            //success (not finished)
            alert("woot!")
            }
         });

Response.Write("<input type='hidden' name='list-value'>");
..

document.forms[0].list-value.value = selectedValue;
document.forms[0].submit();

..

if(Request.Form["list-value"]) != "" { // do something }