Your code is fine. The problem is with the HTML markup. As you have not posted the complete markup, here is what i assume you have missed:
1. A ScriptManager on your aspx page.
2. DropDownList tag is not well formed.
3. UpdatePanel's UpdateMode property is not specified, so by default it is "Always".
Replace your markup with the following and try:
<asp:scriptmanager runat="server" id="ScriptManager1"></asp:scriptmanager>
<asp:updatepanel id="UpdatePanel3" runat="server" updatemode="Conditional"/><contenttemplate>
<asp:DropDownList ID="DropDownList1" runat="server"></DropDownList>