<asp:Content ID="Content1" ContentPlaceHolderID="HeadContent" runat="server">
    <link href="<%= Page.ResolveClientUrl("~/Styles/smoothness/jquery-ui-1.10.4.custom.min.css") %>" rel="stylesheet" />
</asp:Content>
<asp:Content ID="Content2" ContentPlaceHolderID="MainContent" runat="server">
    <script type="text/javascript" src="<%= Page.ResolveClientUrl("~/Scripts/jquery-ui-1.10.4.custom.min.js") %>"></script>
    <script type="text/javascript" src="<%= Page.ResolveClientUrl("~/Scripts/jquery.ui.core.js") %>"></script>
    <script type="text/javascript" src="<%= Page.ResolveClientUrl("~/Scripts/jquery.ui.widget.js") %>"></script>
    <script type="text/javascript" src="<%= Page.ResolveClientUrl("~/Scripts/jquery.ui.datepicker.js") %>"></script>
    <asp:GridView ID="Grid"  runat="server"  AutoGenerateColumns="False" AllowPaging="True" DataKeyNames="UserID" 
        OnRowCommand="Grid_RowCommand" OnRowDataBound="Grid_RowDataBound">
        <Columns>
            <asp:TemplateField HeaderText="ExpirationDate">
                <ItemTemplate>
                    <asp:TextBox ID="DateTextBox" runat="server" Text='<%# Bind("Date", "{0:d}") %>' Class ="DTP"></asp:TextBox>                              
                </ItemTemplate> 
            </asp:TemplateField>
            <asp:TemplateField>
                <ItemTemplate>
                    <asp:LinkButton ID="UpdateButton" CommandName="Update" Text="Update" ButtonType="Button" runat="server" 
                        CommandArgument="<%# ((GridViewRow) Container).RowIndex %>">
                    </asp:LinkButton>
                </ItemTemplate> 
            </asp:TemplateField>             
        </Columns>
    </asp:GridView>
</asp:Content>

 <script type="text/javascript">
        $(function () {
            $('.DTP').datepicker({dateformat: 'dd/mm/yyyy'})
        })
    </script>

protected void Grid_RowCommand(object sender, GridViewCommandEventArgs e)
        {
            e.Handled = true;
            int rowNumber;
            if (int.TryParse((string)e.CommandArgument, out rowNumber))
            {
                switch (e.CommandName)
                {
                    case "Update":
                        TextBox dtb =Grid.Rows[rowNumber].Cells[1].FindControl("DateTextBox") as TextBox;
                        if (dtb == null)
                            return;
                        string dateValueStr = dtb.Text; // здесь получаю пустую строку
                        DateTime date;
                        try
                        {
                            date = Convert.ToDateTime(dateValueStr);
                        }
                        catch (FormatException)
                        {
                            dtb.Text = "Date is not in the proper format";
                            return;
                        }
                        database.Update(Grid.DataKeys[rowNumber].Value.ToString(), date);
                        reload();
                        break;
                }
            }
        }

<script type="text/javascript">
        $(function () {
            $('.DTP').datepicker({
                dateformat: 'dd/mm/yyyy',
                onSelect: function (date, inst) {
                    var date = $('.DTP').datepicker('getDate');
                    $('HiddenField').val = date;
                }

            });
        })
    </script>

+		Request.Form	{__EVENTTARGET=ctl00%24MainContent%24Grid%24ctl02%24UpdateButton&__EVENTARGUMENT=&__VIEWSTATE=7DU1xUODxJWAs1XMHU8lSdH8iTcPsGUCStl6k
%2b%2blx8fk586HZjrhuZpE2U4RJJ8b2M1SKdF5TMo0Kfi0SsLYeSdVueRNBRYYtTRsAxgtmzxOvljdHHRkSUloKrBPLHvwqnixXKZVYoVVrSsME2pwIv
%2fSpcwJRk4l1Tw5vHqWDzN%2bXevzSVNBqtr%2bwVTarGlwhNtk2exQuFyWdIsXnm7umcntROrvj%2fasr%2baFsWwzPt2bI07qlhmUwQLHO23e
LaYURp9ZOdw40Vb0h%2fM%2bWIRse4XP0XNky9c9x0bx6C%2bSaMo8ssYAKpQ2pHzSjbryWn9ZRZ6SPYyc5k0N40SuSujraa%2frKmiPd6wzX4N
NzdAx2mEbU1NsErq7wKdSj31RdBDlNuibLBlhehsZ%2bmm1%2bbLrewgsqoF6owaWzsJTPam1v6URx7dSBda0RUM8UGw30pe%2bflIrYd1e3S6z3u0
WGXeowM5FJkQ%2bhL3%2fK5eAnb%2f6RQVHBZFyNBCjdCeIRVvEkrj7spH7qOqTAnmsKWTxIuh7TmEUky%2bpevsd4jFGZEtrwuBLcf8DYIAPfymt
aYBarRoWJJj1tPpCeuC1Lm52LBUgyLwGzO7UNO2
%2b%2bTI0i%2fhL3wT8Ph6O7cpdpXruvLGrACHPEeSlhSW4QWOocAoHmh50FSLIXmQ5X%2f7EBkwnXe5awY6vwyZqRNQvJVaFfoYJKOaNIJ42oz
ZwHX4tv6Rldy46CB6U9zsa7GqcwEz3yS3d52P13FaYo7otoYD%2fO9e7Z3gakAp1VL0s8XIc9pzyyp8ItPtv0beVTgKkkW8100aoatAvKNmYc0FtbIP
5ret43qtUOiVcQs1cYnnLUBSQIgMsuA4s8MDZqpsqv9eeIuDUcN0wgSD%2bunGwgGOYCVLn4IbDT8wGN10Ydx9iPXv%2fVZXACzenRMA%3d&ctl00%24MainContent%24Grid%24ctl02%24DateTextBox=02%2f11%2f2014&ctl00%24MainContent%24Grid%24ctl02%24HiddenField=&
ctl00%24MainContent%24Grid%24ctl03%24ExpirationDateTextBox=&ctl00%24MainContent%24Grid%24ctl03%24HiddenField=&
__VIEWSTATEENCRYPTED=&
__EVENTVALIDATION=Yy95LcIG5FDergr8Gcrjrss1aS5I3KOedTQE8mKlndQdfdGe1d7gyuj6ZfsiXx87UAGkCVyLE2ufmRmHEgxZTfCj%2fQAtgulq3C
pirGxMEfNhGTAIsEFA9ku%2fudgZ3dUTow6ViGaRvFIAQBUNGf%2fdr53zcE7enmbhPQX%2foIXRdnmNVikF03nhq4gio1oe8%2b84pT8YDmUEOym
MGhp6fAniGjm19Mstxrm1hNgOWSedmpgk8OdPtANVzsVhBHEfGe3pCt7MHg%3d%3d}	System.Collections.Specialized.NameValueCollection 
{System.Web.HttpValueCollection}

string value;
for (int i = 0; i < Grid.Rows.Count; ++i)
{
    TextBox dtb1 = Grid.Rows[i].FindControl("DateTextBox") as TextBox;
    if (dtb1 == null)
        continue;
    value = dtb1.Text;
}