Good for the BBC: BBC News live stats
At CNET News.com, What’s Hot is updated with data hourly, and when new stories are published. Some of the Most Popular data is updated in near-real-time, though most is daily.
For so-close-to-real-time it becomes useless (but still interesting), try Digg Spy.
Showing usage back to the users… that’s fun stuff. And it definitely changes behavior.