Rotate camera around object with Three.js

This is what you want: http://threejs.org/examples/misc_controls_orbit.html

Include the orbit controls (after you have downloaded them):

<script src="js/controls/OrbitControls.js"></script>

Setup the variable:

var controls;

Attach the controls to the camera and add a listener:

controls = new THREE.OrbitControls( camera );
controls.addEventListener( 'change', render );

and in your animate function update the controls:

controls.update();

[Update] controls.autoRotate = true; (tested in v73. Recent versions of OrbitControls.js has added this control.)

Here is a quick hack, in case you don't want to use the OrbitControls for some reason.

            camera.position.copy( target );
            camera.position.x+=Math.sin(camera.rotationy)*3;
            camera.position.z+=Math.cos(camera.rotationy)*3;
            camera.position.y+=cameraHeight; // optional
            tempVector.copy(target).y+=cameraHeight; // the += is optional
            camera.lookAt( tempVector );

camera.rotationy is a copy of the mouse rotation value since we are changing it with the call to lookAt.