Try add AppendDataBoundItems="True"
to the tag and add <asp:ListItem Selected="True"></asp:ListItem>
as an item
<asp:DropDownList ID="DropDownList1" runat="server" AutoPostBack="True"
DataSourceID="SqlDataSource2" DataTextField="director"
DataValueField="director" AppendDataBoundItems="True">
<asp:ListItem Selected="True"></asp:ListItem>
</asp:DropDownList>
<asp:SqlDataSource ID="SqlDataSource2" runat="server" ConnectionString="<%$
ConnectionStrings:dvdsConnectionString %>" ProviderName="<%$
ConnectionStrings:dvdsConnectionString.ProviderName %>"
SelectCommand="SELECT [director] FROM [dvds]">
</asp:SqlDataSource>