How to prevent calling of en event handler twice on fast clicks?

David Walsh has a great solution.

// Returns a function, that, as long as it continues to be invoked, will not
// be triggered. The function will be called after it stops being called for
// N milliseconds. If `immediate` is passed, trigger the function on the
// leading edge, instead of the trailing.
function debounce(func, wait, immediate) {
    var timeout;
    return function() {
        var context = this, args = arguments;
        var later = function() {
            timeout = null;
            if (!immediate) func.apply(context, args);
        };
        var callNow = immediate && !timeout;
        clearTimeout(timeout);
        timeout = setTimeout(later, wait);
        if (callNow) func.apply(context, args);
    };
};

As per edit

You should use .one()

or

You can unbind event on click function

var x = 1;
function myButtonClick() {

    $('#button').unbind('click');

    // Do something
    // Save some data on network
    x++;
    console.log(x);
    $('#button').bind('click', myButtonClick);
}

$('#button').bind('click', myButtonClick);

There are multiple ways of dealing with this:

You can disable/hide the button after the click:

$('#button').attr("disabled", true);

You can also set a timeout on each click to ensure it does not execute again:

var x, y = 1;

$('#button').click(function() {
  if (x) clearTimeout(x);
  x = setTimeout(function() {
     // do the work here
     y++;
     console.log(y);
     // ----------------
  }, 1000);
});

So each time the button is clicked, it will only actually execute the code after a 1000 milliseconds, if the button is clicked in rapid succession, the timeout will just be cleared and start over again.

_{note that the above is untested}

Personally I think the disabled solution is the best as it indicates to the user that he has clicked and something is happening, you can even show a loader next to the button as well.