Transfer speed improvement. If the file you requested was received before to your proxy server, then proxy server will interrupt this file request and you will receive the file directly from proxy. However need to know, you can got the "speed down" effect. This effect appears when your proxy has long answer time because there is slow connection between you and your proxy server;
Security and privacy. Anonymous proxies destroys information about your computer in the requests header. So you can safely surf the net and your information will never be used by hackers and spammers;
Sometimes you encounter some problems while accessing to web server (for example, web-chat). You have mistaken while working with some data and / or the server administrator restricted access from your IP. So you can use the anonymous proxy and try to access again.