There are several uses for anonymous proxies, but one that is not discussed as often (which I needed to make use of today, thus inspiring this entry) is to verify connectivity to your server from outside of your own network.
Other (more common) uses include visiting sites without your IP address being logged and/or visiting sites that you are blocked from accessing directly either by administrative network settings (firewall rules, etc) or a surf-watch type program. In the case of blocking, many of these systems will also try to block access to proxy servers, but there are a lot of them out there, so chances are you can probably find one that isn’t blocked, unless the administrators go through a lot of trouble.
Just don’t try to use it to play online poker.