I came across a site named Black Market Press which had a long list of all the anonymous web surfing portals, these are free which is always good for me:
http://www.blackmarket-press.net/info_01.htm

Of course the best anonymity is provided by using a proxy, and if you're not a techno geek and are using IE then I'll give you some easy step by step guides:

1) go to a sitel listing free public proxies such as http://www.publicproxyservers.com/index.html

2) select one, you can usually test these on their sites to see that they work.

3) Open IE, go to Tools - Internet Options. Select Connections, select Settings, there you will see "proxy server". Simply type in the IP of the proxy you picked earlier, and check the box to use it. Now when you are surfing you are shielding your IP.

4) To check its actually working go to a site that displays your IP, such as http://www.myipaddress.com/

5) You are done, this gives you a minimal level of privacy. You won't be protected from sites exploiting java scripts to obtain your IP, if that is a major concern you will need to step up to using a good socks proxy - but that is a much more complex procedure saved for another post!