URL Snooper is a free Windows software that lets you monitor your network connections and see the addresses of all the files that are downloaded to your computer and all the addresses from HTML files.
But the software is also useful if you want to see the files downloaded by a program you've just installed. Or if you're wondering why Google Desktop needs an Internet connection. You can see in the screenshot above that Google Desktop connects to google.com to read a list of localized domains, the files for the Safe Browsing feature and to download information necessary for the gadgets (weather, news, etc.).