Zend's documentation isn't really clear on this.
The problem is that, by default, Zend automatically renders a view at the end of each controller action. If you're using a layout - and why wouldn't you? - it also renders that. This is fine for normal Web pages, but when you're sending an AJAX response you don't want all that. How do you prevent Zend from auto-rendering on an action-by-action basis?
Call this code from within whatever Action(s) is/are going to be sending AJAX responses:
$this->_helper->layout->disableLayout();
$this->_helper->viewRenderer->setNoRender(TRUE);
This disables the Layout engine for that action, and it turns off automatic view rendering for that action. You can then just "echo" whatever you want your AJAX output to be, without worrying about the normal view/layout stuff getting sent along for the ride.