Detect clicked object in THREE.js

Depends on what kind of camera are you using.

1) PerspectiveCamera: is ok link that Mr.doob provides.
2) OrthographicCamera: is quite different:

var init = function() {
  camera = new THREE.OrthographicCamera( SCREEN_WIDTH / - 2, SCREEN_WIDTH / 2, SCREEN_HEIGHT / 2, SCREEN_HEIGHT / - 2, NEAR, FAR);
  document.addEventListener( 'mousedown', onDocumentMouseDown, false );
}

function onDocumentMouseDown( e ) {
  e.preventDefault();
  var mouseVector = new THREE.Vector3();
  mouseVector.x = 2 * (e.clientX / SCREEN_WIDTH) - 1;
  mouseVector.y = 1 - 2 * ( e.clientY / SCREEN_HEIGHT );
  var raycaster = projector.pickingRay( mouseVector.clone(), camera );
  var intersects = raycaster.intersectObject( TARGET );
  for( var i = 0; i < intersects.length; i++ ) {
    var intersection = intersects[ i ],
    obj = intersection.object;
    console.log("Intersected object", obj);
  }
}

Check out this one:

var camera = new THREE.PerspectiveCamera(45, window.innerWidth / window.innerHeight, 1, 5000);
var object; //your object

document.addEventListener('mousedown', onMouseDown, false);

function onMouseDown(e) {
    var vectorMouse = new THREE.Vector3( //vector from camera to mouse
        -(window.innerWidth/2-e.clientX)*2/window.innerWidth,
        (window.innerHeight/2-e.clientY)*2/window.innerHeight,
        -1/Math.tan(22.5*Math.PI/180)); //22.5 is half of camera frustum angle 45 degree
    vectorMouse.applyQuaternion(camera.quaternion);
    vectorMouse.normalize();        

    var vectorObject = new THREE.Vector3(); //vector from camera to object
    vectorObject.set(object.x - camera.position.x,
                     object.y - camera.position.y,
                     object.z - camera.position.z);
    vectorObject.normalize();
    if (vectorMouse.angleTo(vectorObject)*180/Math.PI < 1) {
        //mouse's position is near object's position

    }
}

Checks for intersection of the mouse and any of the Cubes in 3d space and alters it's color. Maybe this help you.

I ran into problems trying to implement this for a canvas which does not take up the entire width and height of the screen. Here is the solution I found works quite well.

Initialize everything on an existing canvas:

var init = function() {
  var canvas_model = document.getElementById('model')
  var viewSize = 50 // Depending on object size, canvas size etc.
  var camera = new THREE.OrthographicCamera(-canvas_model.clientWidth/viewSize, canvas_model.clientWidth/viewSize, canvas_model.clientHeight/viewSize, -canvas_model.clientHeight/viewSize, 0.01, 2000),
}

Add an event listener to the canvas:

canvas_model.addEventListener('click', function(event){
  var bounds = canvas_model.getBoundingClientRect()
  mouse.x = ( (event.clientX - bounds.left) / canvas_model.clientWidth ) * 2 - 1;
  mouse.y = - ( (event.clientY - bounds.top) / canvas_model.clientHeight ) * 2 + 1;
  raycaster.setFromCamera( mouse, camera );
  var intersects = raycaster.intersectObjects(scene.children, true);
  if (intersects.length > 0) {
     // Do stuff
  }
}, false)

Or for a 'touchstart' event, change the lines calculating the mouse.x and mouse.y into:

mouse.x = ( (event.touches[0].clientX - bounds.left) / canvas_model.clientWidth ) * 2 - 1;
mouse.y = - ( (event.touches[0].clientY - bounds.top) / canvas_model.clientHeight ) * 2 + 1;