As long as support for the "URL fopen wrapper" is enabled when you configure PHP (which it is unless you explicitly pass the --disable-url-fopen-wrapper flag to configure (for versions up to 4.0.3) or set allow_url_fopen to off in php.ini (for newer versions), you can use HTTP and FTP URLs with most functions that take a filename as a parameter, including the require() and include() statements.
For example, you can use this to open a file on a remote web server, parse the output for the data you want, and then use that data in a database query, or simply to output it in a style matching the rest of your website.
You can also write to files on an FTP as long you connect as a user with the correct access rights, and the file doesn't exist already. To connect as a user other than 'anonymous', you need to specify the username (and possibly password) within the URL, such as 'ftp://user:password@ftp.example.com/path/to/file'. (You can use the same sort of syntax to access files via HTTP when they require Basic authentication.)
Note: You might get the idea from the example above to use this technique to write to a remote log, but as mentioned above, you can only write to a new file using the URL fopen() wrappers. To do distributed logging like that, you should take a look at syslog().