Hi  rajeshR2,
I have created sample code which full-fill your requirement.
HTML
<div>
    <asp:TextBox ID="txtUserId" Height="30px" runat="server" />
    <img src="loader.gif" id="loader" style="display: none" height="34px" alt="" />
    <asp:Label ID="lblStatus" runat="server" />
</div>
<div>
<script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1.9.1/jquery.min.js"></script>
<script type="text/javascript">
    $(function () {
        $('[Id*=txtUserName]').keyup(function (event) {
            if ($(this).val() != "") {
                $('[Id*=loader]').show();
                SetData();
                if (event.which === 13) {
                    $('[Id*=loader]').hide();
                }
            }
            else {
                $('[Id*=loader]').hide();
                $('[Id*=lblStatus]').text('');
            }
        });
        $('[Id*=txtUserId]').blur(function () {
            $('[Id*=loader]').hide();
        });
    });
    function SetData() {
        var obj = {};
        obj.name = $.trim($("[id*=txtUserName]").val());
        $.ajax({
            type: "POST",
            url: "ValidateUser.asmx/ValidateUsers",
            data: JSON.stringify(obj),
            contentType: "application/json; charset=utf-8",
            dataType: "json",
            success: function (r) {
                if (r.d != '') {
                    $('[Id*=lblStatus]').text('Not Available...');
                    $('[Id*=lblStatus]').css("color", "red");
                }
                else {
                    $('[Id*=lblStatus]').text('Available');
                    $('[Id*=lblStatus]').css("color", "green");
                }
            }
        });
    }
</script>
</div>
WebService.asmx
[WebMethod]
public Boolean ValidateUsers(string name)
{
    Boolean result = false;
    string query = "SELECT CustomerId, Name FROM Customers WHERE Name='" + name + "'";
    string constr = ConfigurationManager.ConnectionStrings["constr"].ConnectionString;
    using (SqlConnection con = new SqlConnection(constr))
    {
        using (SqlCommand cmd = new SqlCommand(query))
        {
            cmd.CommandType = CommandType.Text;
            cmd.Connection = con;
            con.Open();
            SqlDataReader idr = cmd.ExecuteReader();
            if (idr.HasRows)
            {
                result = true;
            }
            con.Close();
            return result;
        }
    }
}