Here are some examples:
Another very interesting page I found on Alexa is a live demo of what you can do with Alexa’s API. Derrick Pallas built a demo application with which you can search the robots.txt files of all the websites in Alexa’s index. Now let’s see what websites disallow Googlebot ? Or the MediaPartners Bot ? Find websites that spam, disallow the AdsBot (arbitrage) etc.
Perhaps you want to search pictures that were taken with a specific digital camera model ?
The possibilities are endless.