Handling "onclick" event with pure JavaScript

All browsers support this (see example here):

mySelectedElement.onclick = function(e){
    //your handler here
}

However, sometimes you want to add a handler (and not change the same one), and more generally when available you should use addEventListener (needs shim for IE8-)

mySelectedElement.addEventListener("click",function(e){
   //your handler here
},false);

Here is a working example:

var button = document.getElementById("myButton");
button.addEventListener("click",function(e){
    button.disabled = "true";
},false);

And html:

<button id='myButton'>Hello</button>

(fiddle)

Here are some useful resources:

• addEventListener on mdn
• The click event in the DOM specification
• Click example in the MDN JavaScript tutorial

Benjamin's answer covers quite everything. However you need a delegation model to handle events on elements that were added dynamically then

document.addEventListener("click", function (e) {
    if (e.target.id == "abc") {
        alert("Clicked");
    }
});

For IE7/IE8

document.attachEvent('onclick', function (e) {
    if (window.event.srcElement == "abc") {
        alert("Clicked");
    }
});