Detect click outside element (vanilla JavaScript)

How about this:

jsBin demo

document.onclick = function(event){
  var hasParent = false;
    for(var node = event.target; node != document.body; node = node.parentNode)
    {
      if(node.id == 'div1'){
        hasParent = true;
        break;
      }
    }
  if(hasParent)
    alert('inside');
  else
    alert('outside');
} 

You need to handle the click event on document level. In the event object, you have a target property, the inner-most DOM element that was clicked. With this you check itself and walk up its parents until the document element, if one of them is your watched element.

See the example on jsFiddle

document.addEventListener("click", function (e) {
  var level = 0;
  for (var element = e.target; element; element = element.parentNode) {
    if (element.id === 'x') {
      document.getElementById("out").innerHTML = (level ? "inner " : "") + "x clicked";
      return;
    }
    level++;
  }
  document.getElementById("out").innerHTML = "not x clicked";
});

As always, this isn't cross-bad-browser compatible because of addEventListener/attachEvent, but it works like this.

A child is clicked, when not event.target, but one of it's parents is the watched element (i'm simply counting level for this). You may also have a boolean var, if the element is found or not, to not return the handler from inside the for clause. My example is limiting to that the handler only finishes, when nothing matches.

Adding cross-browser compatability, I'm usually doing it like this:

var addEvent = function (element, eventName, fn, useCapture) {
  if (element.addEventListener) {
    element.addEventListener(eventName, fn, useCapture);
  }
  else if (element.attachEvent) {
    element.attachEvent(eventName, function (e) {
      fn.apply(element, arguments);
    }, useCapture);
  }
};

This is cross-browser compatible code for attaching an event listener/handler, inclusive rewriting this in IE, to be the element, as like jQuery does for its event handlers. There are plenty of arguments to have some bits of jQuery in mind ;)

Add an event listener to document and use Node.contains() to find whether the target of the event (which is the inner-most clicked element) is inside your specified element. It works even in IE5

const specifiedElement = document.getElementById('a')

// I'm using "click" but it works with any event
document.addEventListener('click', event => {
  const isClickInside = specifiedElement.contains(event.target)

  if (!isClickInside) {
    // The click was OUTSIDE the specifiedElement, do something
  }
})

var specifiedElement = document.getElementById('a');

//I'm using "click" but it works with any event
document.addEventListener('click', function(event) {
  var isClickInside = specifiedElement.contains(event.target);
  if (isClickInside) {
    alert('You clicked inside A')
  } else {
    alert('You clicked outside A')
  }
});

div {
  margin: auto;
  padding: 1em;
  max-width: 6em;
  background: rgba(0, 0, 0, .2);
  text-align: center;
}

Is the click inside A or outside?
<div id="a">A
  <div id="b">B
    <div id="c">C</div>
  </div>
</div>