When you draw to a canvas element, you are simply drawing a bitmap in immediate mode.

The elements (shapes, lines, images) that are drawn have no representation besides the pixels they use and their colour.

Therefore, to get a click event on a canvas element (shape), you need to capture click events on the canvas HTML element and use some math to determine which element was clicked, provided you are storing the elements' width/height and x/y offset.

To add a click event to your canvas element, use...

canvas.addEventListener('click', function() { }, false);

To determine what element was clicked...

var elem = document.getElementById('myCanvas'),

    elemLeft = elem.offsetLeft,

    elemTop = elem.offsetTop,

    context = elem.getContext('2d'),

    elements = [];

// Add event listener for `click` events.

elem.addEventListener('click', function(event) {

    var x = event.pageX - elemLeft,

        y = event.pageY - elemTop;

    // Collision detection between clicked offset and element.

    elements.forEach(function(element) {

        if (y > element.top && y < element.top + element.height

            && x > element.left && x < element.left + element.width) {

            alert('clicked an element');

        }

    });

}, false);

// Add element.

elements.push({

    colour: '#05EFFF',

    width: 150,

    height: 100,

    top: 20,

    left: 15

});

// Render elements.

elements.forEach(function(element) {

    context.fillStyle = element.colour;

    context.fillRect(element.left, element.top, element.width, element.height);

});​

jsFiddle.

This code attaches a click event to the canvas element, and then pushes one shape (called an element in my code) to an elements array. You could add as many as you wish here.

The purpose of creating an array of objects is so we can query their properties later. After all the elements have been pushed onto the array, we loop through and render each one based on their properties.

When the click event is triggered, the code loops through the elements and determines if the click was over any of the elements in the elements array. If so, it fires an alert(), which could easily be modified to do something such as remove the array item, in which case you'd need a separate render function to update the canvas.

For completeness, why your attempts didn't work...

elem.onClick = alert("hello world"); // displays alert without clicking

This is assigning the return value of alert() to the onClick property of elem. It is immediately invoking the alert().

elem.onClick = alert('hello world');  // displays alert without clicking

In JavaScript, the ' and " are semantically identical, the lexer probably uses ['"] for quotes.

elem.onClick = "alert('hello world!')"; // does nothing, even with clicking

You are assigning a string to the onClick property of elem.

elem.onClick = function() { alert('hello world!'); }; // does nothing

JavaScript is case sensitive. The onclick property is the archaic method of attaching event handlers. It only allows one event to be attached with the property and the event can be lost when serialising the HTML.

elem.onClick = function() { alert("hello world!"); }; // does nothing

Again, ' === ".