Using AJAX to Dynamically Fill a Dropdown VB.Net JQuery

First off, you do not need to serialize the data coming back from your ASP.NET AJAX Page Method, as it JSON serializes the data by default.

Second, why are you not returning a type from you method? It is a Function and there is no return type declared. It appears you want to return a List(Of T) so that you can loop through the results client-side.

Here is an example page method that returns the current time as a String:

<WebMethod> _
Public Shared Function GetDate() As String
    Return DateTime.Now.ToString()
End Function

Please read this to become more familiar with Using jQuery to directly call ASP.NET AJAX page methods

Here's the final jQuery code:

<%@ Page Title="" Language="vb" AutoEventWireup="false" MasterPageFile="~/Site.Master"      CodeBehind="Request.aspx.vb" Inherits="NDBEDP.Request" MaintainScrollPositionOnPostback="true" %>
<asp:Content ID="Content1" ContentPlaceHolderID="HeadContent" runat="server">
</asp:Content>
<asp:Content ID="Content2" ContentPlaceHolderID="FeaturedContent" runat="server">
</asp:Content>
<asp:Content ID="Content3" ContentPlaceHolderID="MainContent" runat="server">
    <script type="text/javascript">
        $('.entityDrop').live('change', function (event) {
            loadStateDrop()
        });

        var loadStateDrop = function () {
            var data = "{'entity':'"+ $('#<%=ddlEntity.ClientID%> option:selected').val()+"'}"
            $.ajax({
                type: "POST",
                url: "Request.aspx/loadStates",
                datatype: "JSON",
                data: data,
                contentType: "application/json; charset=utf-8",
                success: function (list) {
                    $('.stateDrop').empty();
                    if (list.hasOwnProperty("d")) {
                         $.each(list.d, function (key, value) {
                             var optn = document.createElement("OPTION");
                             optn.text = key;
                             optn.value = value;
                             $('.stateDrop').append(optn);
                         });
                     }
                     else {
                         $.each(list, function (key, value) {
                             var optn = document.createElement("OPTION");
                             optn.text = key;
                             optn.value = value;
                             $('.stateDrop').append(optn);
                         });
                     }
                },
                error: function (jqXHR, textStatus, errorThrown) {
                    alert("Error updating dropdowns: " + errorThrown);
                }
            });
        };
    </script>
    <asp:panel ID="userInput" runat="server">
        <asp:panel id="userInformation" runat="server" BorderStyle="None" style="margin-bottom: 0px">
            <asp:DropdownList cssClass="entryField, entityDrop" ID="ddlEntity" runat="server" Width="95%"></asp:DropdownList>
            <asp:DropDownList cssClass="entryField, stateDrop" ID="ddlExpenseState" runat="server" Width="18%"></asp:DropDownList>
            <asp:DropDownList ID="ddlExpensePeriod" runat="server" cssClass="entryField" Width="50%"></asp:DropDownList>
            <asp:DropDownList ID="ddlExpenseYear" runat="server" cssClass="entryField" Width="20%"></asp:DropDownList>
        </asp:panel>
    </asp:panel>
</asp:Content>

This is my VB.Net code (I probably don't need all of the includes):

Imports NDBEDP.StringExtensions
Imports NDBEDP.DropdownExtensions
Imports NDBEDP.GridViewExtensions
Imports System.IO
Imports System.Web.Services
Imports System.Web.Script.Services
Imports System.Web.Script.Serialization

Public Class Request
    Inherits System.Web.UI.Page

    <WebMethod()> _
    Public Shared Function loadStates(entity As Integer) As Dictionary(Of String, Integer)
        Dim expenseStates As DataSet = (New RequestBus).getExpenseStates(entity)
        Dim returnStates As New Dictionary(Of String, Integer)
        For i As Integer = 0 To expenseStates.Tables(0).Rows.Count - 1
            returnStates.Add(expenseStates.Tables(0).Rows(i).Item("StateAbbr"), expenseStates.Tables(0).Rows(i).Item("StateID"))
        Next
        Return returnStates
    End Function
End Class

Edited to take advantage of this article