add event listener on elements created dynamically

It sounds like you need to pursue a delegation strategy without falling back to a library. I've posted some sample code in a Fiddle here: http://jsfiddle.net/founddrama/ggMUn/

The gist of it is to use the target on the event object to look for the elements you're interested in, and respond accordingly. Something like:

document.querySelector('body').addEventListener('click', function(event) {
  if (event.target.tagName.toLowerCase() === 'li') {
    // do your action on your 'li' or whatever it is you're listening for
  }
});

CAVEATS! The example Fiddle only includes code for the standards-compliant browsers (i.e., IE9+, and pretty much every version of everyone else) If you need to support "old IE's" attachEvent, then you'll want to also provide your own custom wrapper around the proper native functions. (There are lots of good discussions out there about this; I like the solution Nicholas Zakas provides in his book Professional JavaScript for Web Developers.)

Depends on how you add new elements.

If you add using createElement, you can try this:

var btn = document.createElement("button");
btn.addEventListener('click', masterEventHandler, false);
document.body.appendChild(btn);

Then you can use masterEventHandler() to handle all clicks.

An obscure problem worth noting here may also be this fact I just discovered:

If an element has z-index set to -1 or smaller, you may think the listener is not being bound, when in fact it is, but the browser thinks you are clicking on a higher z-index element.

The problem, in this case, is not that the listener isn't bound, but instead it isn't able to get the focus, because something else (e.g., perhaps a hidden element) is on top of your element, and that what get's the focus instead (meaning: the event is not being triggered). Fortunately, you can detect this easily enough by right-clicking the element, selecting 'inspect' and checking to see if what you clicked on is what is being "inspected".

I am using Chrome, and I don't know if other browsers are so affected. But, it was hard to find because functionally, it resembles in most ways the problem with the listener not being bound. I fixed it by removing from CSS the line: z-index:-1;