Often I want to inspect an element (e.g. tooltip) that only appears when another element is mouse overed/entered. The element that appears, is made visible via jQuery\'s mousee
It's fairly easy in Chrome 38.0.2094.0.
Here's what it'll look like:

Step-by-step:
If the tooltip shows up because of CSS, here's what you can do in that case:

Step-by-step:
Both Safari's and Chrome's Web Inspector offers checkboxes where you can toggle the :active, :focus, :hover and :visited state of an element. Using those might be even easier.
Safari:

Chrome:

While @SomeGuy's answer is excellent (t-up for animated gifs), as an alternative you can always do it programmatically. Just pop open the console and type in the event name
document.getElementById('id').dispatchEvent(new Event('event-type'));
(with pure javascript specific syntax may vary by browser)
Even easier with jQuery:
$('#id').trigger('event-type');
In your example (http://getbootstrap.com/javascript/#tooltips), open the console and type in, for example:
$("button:contains('Tooltip on right')").mouseenter();
And the tooltip appears in the DOM and can be manually inspected/modified:
<div style="top: 14406.9px; left: 1048.25px; display: block;"
id="tooltip952596" class="tooltip fade right in" role="tooltip">
<div style="" class="tooltip-arrow"></div>
<div class="tooltip-inner">Tooltip on right</div></div>
As in the comments, if you move the mouse pointer over the page frame, you can trigger other events such as mouseout. To prevent this you can press F8 (as in the acc. answer) or type debugger; (which is its script equivalent)
There's also another tricky way to do it :
Your tooltip will stay visible, you will then be able to inspect it in the Element tab.
Tested on Chrome. Doesn't seem to work on Firefox.