A fully web-based proxy cannot accept connections as if it was an HTTP or SOCKS proxy. It has to use some hacks (typically using URL redirects) to route the traffic to you. Compatibility with JS/ajax-intensive web apps is quite tricky to achieve.
Glype [1] is an example of web proxy that provides rewriting and customizable plugins to improve compatibility with complex web apps. Not free software but comes with source code (PHP).