<asp:DropDownList ID="DropDownList1" runat="server" Height="34px" 
        onselectedindexchanged="DropDownList1_SelectedIndexChanged" Width="196px">
        <asp:ListItem>a</asp:ListItem>
        <asp:ListItem>b</asp:ListItem>
        <asp:ListItem>c</asp:ListItem>
    </asp:DropDownList>
    

    

    <asp:ListBox ID="ListBox1" runat="server" Height="107px" Width="190px">
    </asp:ListBox>

protected void DropDownList1_SelectedIndexChanged(object sender, EventArgs e)
        {
            string str = DropDownList1.SelectedItem.Text;
            ListBox1.Items.Add(str);
        }