How I can add and remove the attribute "readonly"?

Yes, finally I've found the solution. I've used onChange function.

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.4.2/jquery.min.js"></script>
<script>
//$(document).ready(function() {
function check_city(city_value) {
  //Check City Value
  city_value = $("#city").val();
  if( city_value == "0") {
     $("#state").attr("readonly", true);
     //$("#rate").attr("readonly", "readonly");   
  } else {
     $("#state").attr("readonly", false);
     //$("#state").removeAttr("readonly");
     //document.getElementById("state").removeAttribute("readonly",0);
     //get_states(city_value);
  }
 /***
  //Check State Value
  var state_value = parseInt($('#state').val());
  if( state_value == 0) {
      $('#rate').attr('readonly', true); 
  } else {
     $('#rate').attr('readonly', false);
  }
  ***/
//});
}
</script>

<td><select name="city" id="city" onChange="check_city(this.value)">
<option selected value="0">PLEASE_SELECT_TEXT</option>
<option value="Antalya">Antalya</option>
<option value="Bodrum">Bodrum</option>
<option value="Istanbul">Istanbul</option>
</select>&nbsp;</td>
<td><div id="states"><input type="text" name="state" value="FORCE_FOR_SELECT" readonly id="state"></div></td>

While the readonly property takes a boolean value, the readonly attribute takes a string value. You should use the code that you have commented out:

$("#rate").attr("readonly", "readonly");

Works fine here in all major browsers I have. Here's an SSCCE:

<!doctype html>
<html lang="en">
    <head>
        <title>SO question 2496443</title>
        <script src="http://code.jquery.com/jquery-latest.min.js"></script>
        <script>
            $(document).ready(function() {
                $('#toggle').click(function() {
                    $('#foo').attr('readonly', !$('#foo').attr('readonly'));
                });
            });
        </script>
        <style>
            input[readonly] { 
                background: lightgray;
            }
        </style>
    </head>
    <body>
        <input id="foo">
        <button id="toggle">toggle readonly</button>
    </body>
</html>

Toggling it turns the background gray (although not all browsers do that) and the input is uneditable (this is consistent among all webbrowsers). So your problem lies somewhere else. You're probably using a poor doctype and possibly also in combination with a poor webbrowser.