Use promises

The Promise API is a new feature of ECMAScript 6, but it has good browser support already. There are also many libraries which implement the standard Promises API and provide additional methods to ease the use and composition of asynchronous functions (e.g. bluebird).

Promises are containers for future values. When the promise receives the value (it is resolved) or when it is cancelled (rejected), it notifies all of its "listeners" who want to access this value.

The advantage over plain callbacks is that they allow you do decouple your code and they are easier to compose.

Here is a simple example of using a promise:

function delay() {
  // `delay` returns a promise
  return new Promise(function(resolve, reject) {
    // Only `delay` is able to resolve or reject the promise
    setTimeout(function() {
      resolve(42); // After 3 seconds, resolve the promise with value 42
    }, 3000);
  });
}

delay().then(function(v) { // `delay` returns a promise
  console.log(v); // Log the value once it is resolved
}).catch(function(v) {
  // Or do something else if it is rejected 
  // (it would not happen in this example, since `reject` is not called).
});

Applied to our Ajax call we could use promises like this:

function ajax(url) {
  return new Promise(function(resolve, reject) {
    var xhr = new XMLHttpRequest();
    xhr.onload = function() {
      resolve(this.responseText);
    };
    xhr.onerror = reject;
    xhr.open('GET', url);
    xhr.send();
  });
}

ajax("/echo/json").then(function(result) {
  // Code depending on result
}).catch(function() {
  // An error occurred
});

Describing all the advantages that promises offer is beyond the scope of this answer, but if you write new code, you should seriously consider them. They provide a great abstraction and separation of your code.

More information about promises: HTML5 rocks - JavaScript Promises