Two weeks ago, Google Analytics launched real-time stats. This feature is not enabled for everyone yet, but you can request an invitation using this form. After receiving the invitation, you need to switch to the new Analytics interface, select a site, go to the "Home" tab and click "Real-Time (Beta) / Overview".
I must say that this feature is addictive because it shows a lot of information about your site in real-time. You can find the number of active visitors, the number of pageviews, the top referrals and the top active pages. There's also a map that highlights the cities where your visitors are coming from. And all this information is updated so frequently that it's difficult to keep up with the ever changing stats.
Google Analytics is great for the intuitive reports and the advanced filters that help you understand traffic fluctuations, but a lot of people will use the service more often because of the real-time stats. They're constantly changing, they're mesmerizing and empowering.