Create a custom callback in JavaScript

All I need to do is to execute a callback function when my current function execution ends.

function LoadData() 
{
    alert('The data has been loaded');
    //Call my callback with parameters. For example,
    //callback(loadedData , currentObject);
}

A consumer for this function should be like this:

object.LoadData(success);

function success(loadedData , currentObject) 
{
  //Todo: some action here 
}

How do I implement this?

Actually, your code will pretty much work as is, just declare your callback as an argument and you can call it directly using the argument name.

The basics

function doSomething(callback) {
    // ...

    // Call the callback
    callback('stuff', 'goes', 'here');
}

function foo(a, b, c) {
    // I'm the callback
    alert(a + " " + b + " " + c);
}

doSomething(foo);

That will call doSomething, which will call foo, which will alert "stuff goes here".

Note that it's very important to pass the function reference (foo), rather than calling the function and passing its result (foo()). In your question, you do it properly, but it's just worth pointing out because it's a common error.

More advanced stuff

Sometimes you want to call the callback so it sees a specific value for this. You can easily do that with the JavaScript call function:

function Thing(name) {
    this.name = name;
}
Thing.prototype.doSomething = function(callback) {
    // Call our callback, but using our own instance as the context
    callback.call(this);
}

function foo() {
    alert(this.name);
}

var t = new Thing('Joe');
t.doSomething(foo);  // Alerts "Joe" via `foo`

You can also pass arguments:

function Thing(name) {
    this.name = name;
}
Thing.prototype.doSomething = function(callback, salutation) {
    // Call our callback, but using our own instance as the context
    callback.call(this, salutation);
}

function foo(salutation) {
    alert(salutation + " " + this.name);
}

var t = new Thing('Joe');
t.doSomething(foo, 'Hi');  // Alerts "Hi Joe" via `foo`

Sometimes it's useful to pass the arguments you want to give the callback as an array, rather than individually. You can use apply to do that:

function Thing(name) {
    this.name = name;
}
Thing.prototype.doSomething = function(callback) {
    // Call our callback, but using our own instance as the context
    callback.apply(this, ['Hi', 3, 2, 1]);
}

function foo(salutation, three, two, one) {
    alert(salutation + " " + this.name + " - " + three + " " + two + " " + one);
}

var t = new Thing('Joe');
t.doSomething(foo);  // Alerts "Hi Joe - 3 2 1" via `foo`

It is good practice to make sure the callback is an actual function before attempting to execute it:

if (callback && typeof(callback) === "function") {

  callback();
}

My 2 cent. Same but different...

<script>
    dosomething("blaha", function(){
        alert("Yay just like jQuery callbacks!");
    });


    function dosomething(damsg, callback){
        alert(damsg);
        if(typeof callback == "function") 
        callback();
    }
</script>

function loadData(callback) {

    //execute other requirement

    if(callback && typeof callback == "function"){
        callback();
   }
}

loadData(function(){

   //execute callback

});

   function callback(e){
      return e;
   }
    var MyClass = {
       method: function(args, callback){
          console.log(args);
          if(typeof callback == "function")
          callback();
       }    
    }

==============================================

MyClass.method("hello",function(){
    console.log("world !");
});

==============================================

Result is:

hello world !