Anyone who has administered or moderated an IRC channel, bulletin board site or similar will recognize the scenario. A troublemaker, whether because what they're posting is abusive, illegal or just simply against the terms of service of the site or server in question is banned and reappears under a new identity and new IP address, courtesy of a proxy that has been left wide open and where the system administrator is, unsurprisingly, reticent in responding to your emails pleading with them to tighten up their security.

Nonetheless, whatever the practical reason, there may be a business case for checking that users connecting to your Web server are not using such an open proxy. Ultimately the means of doing this is simply to test the IP address that they claim to be coming through and see if it will accept you without authentication.