Sending a integer value to php with javascript and returning values

Within your php file, you forgot a break statement within the case 2, that results with a problem.

if(isset($_POST["komut"]))
{
    switch($_POST["komut"])
    {
        case 1:
            echo "This is one";
            break;
        case 2:
            echo "This is two";
            break;
        default:
            echo "Something is wrong";
            break;
    }
}

Also if I were you I'd reconfigure the html like below, but it's up to you. Thus, to define a variable in javascript, you need to use var keyword.

<div id="klikme">
    KLİK ME!
</div>
<div id="output"></div>
<script type="text/javascript">
    var sayac = 1;
    $(document).delegate("#klikme", "click", function() {
        $.post('sayac.php',{"komut": sayac++ }).success(function(data){
            $('#output').html(data);
        });
    });
</script>

Correct version of this script is:

<script src="https://ajax.googleapis.com/ajax/libs/jquery/1/jquery.min.js"></script>
<script> 
(function($) {
  var counter = 1;
  $(document).ready(function() {
    $('#clickme').on("click", function(){
      counter++; // first increment counter
    	$.post('http://localhost/index.php', {"counter" : counter }, function(data) { 
    		$('#output').html(data);
    	});
    	$('#counter').text(counter);
    });
  });
})(jQuery);
</script>
<div id="clickme">Click ME!</div>
<div id="counter">1</div>
<div id="output"><?php include 'index.php'; ?></div>

Notice few things:

• Whole code is close in function (function($) { }(jQuery) it's because of variable scope
• A page can't be manipulated safely until the document is "ready" we have everything closed in $(document).ready(function() { });
• We are using on() instead of delegate() since jQuery 1.7
• It's safer use whole url when you call $.post()

And your PHP file can be like this (see $_REQUEST):

<strong><?php echo intval($_REQUEST['counter']); ?></strong>

I would wait until the document has finished loading before binding your JavaScript events to the page, this is because in some browsers your code will begin executing before the element you are trying to bind too exists meaning your event is not binded.

I would re-write your JS code like so:

var sayac = 1;
$(document).ready(function() {

    $(document).delegate("#klikme", "click", function() {
        $.post('sayac.php',{"komut": sayac }, function(data){
            $('#output').html(data);
        });
        sayac = sayac + 1;
    });
});

However, given the nature of delegate you would believe this not to be a problem - and the likely cause is the JS error from int sayac, as mentioned below.

There are 2 minor syntax errors in your code, that broke it:

Javascript:

//This is not C, define a variable with "var", not int sayac
var sayac = 1;

PHP:

switch($_POST["komut"])
{
    case "1":
        echo "This is one";
        break;
    case "2":
        echo "This is two";
        break;//<- put "break" here to print only the message for 2
    default: //<- put ":" here
        echo "Something is wrong";
        break;
}