It's very cool to see things as they happen. Google has at Googleplex a big display that shows live queries from all the world, but they didn't make it available online for privacy reasons. But there's an alternative: Dogpile, a small metasearch engine, shows unedited real-time Web searches.
To see all the recent Flickr photos that also have geographical information, there's Flickrvision. All the photos are placed on a Google map and they change very quickly. It's an addictive way to learn about diversity, people and to destroy the artificial borders between countries.
If you have a site and want a real-time view of your visitors, Clicky has a "spy" feature "that shows you actions on your web site as they are happening, delayed no more than five seconds" (here's a demo). You'll spend hours finding who visits your site and why.
Digg Spy is another prime example of live view of a site: see all the submissions, diggs, buries and comments from Digg. Gianni Milanesi even tried to reverse engineer the system and provides the code for a simple Digg Spy clone.
To visualize the blogosphere activity, Twingly Screensaver uses a lot of graphical resources, but is cool enough to let you focus on a region.
All these tools show live data and the feeling of immediacy makes them almost hypnotic. You don't see the big the picture, but you're flooded with surprising details that capture your attention.