One of the most extravagant uses of Internet connected host computers is the SETI@home project. SETI is the organization that is searching for signals from space to determine if life exists elsewhere in the universe.
They allow Internet users to download SETI software to assist in listening to, or rather processing, signals that come through the SETI project.
Thousands of signals come through and when the user’s software detects anything unusual it notifies SETI and they investigate further. It’s basically one big, massive distributed computing project, or what is commonly nowadays called cloud computing.
I have this software installed on my home computer, and it operates in the background displaying these weird sine waves. I don't know if we've found ET yet, but I'm glad to play a small part regardless.