A web proxy can be used for several purposes, including caching, censorware, malware filtering, reformatting or the well known proxy avoidance - this is a special subcase, the CGI proxy.
The caching webproxy is used for a more efficient access to remote resources - files, web pages which are otherway located on remote servers. A copy of these is locally stored and returned at every request that needs it, and there are specific algorithms to mantain the list of the copies both consistent and optimized.
The censorware proxy filters the offensive web content, restraining the access to specific resources "black listed".
The web proxied used to reformat the requested pages are mainly useful when those sites are requested by a phone, PDA etc. and they convert the otherwise computer-only browser understandable form into one that can be 'read' by the specified devices' browsers too.
Even their efficiency can't be mentained on a long-term basis, the proxies that act as a protective filter that retains the viruses and other hostile content are sometimes used by nwetwork administrators.
Finally, the CGI web proxies are the most searched for, especially the free ones. They allow access to a website through them, eluding the interdiction in visiting those sites (at school or office) and offering a certain degree of privacy, by hiding he users' IPs from the visited sites. However, the free CGI proxy can be a danger itself, as the data that passes through it can be accessed by the proxy's administrator; in the case of a insecure connection, this can lead to serious trouble, especially if the data we're talking about includes usernames, passwords, credit card numbers and so on.