Complete Anonymous Web Surfing Checklist
Web Browser - this is perhaps the easiest thing to protect. Your browser will keep a history of web pages you visit and cookies to speed up your browsing. Enabling the 'privacy mode' or deleting the history will clear these traces.
Logging at ISP - yep the one most people forget about but the most complete record of all your browsing on the internet. Every communication and request is logged by your ISP linked to your account. It doesn't matter if you're using an anonymous proxy - all the data goes through your ISP - the only way around this is to either encrypt your connection (or use somebody's web connection - and you shouldn't do that as it's stealing !)
Logging on Web Servers - every web server you visit records your IP address. This can be linked back to your computer fairly easily. The usual method for bypassing this logging is to surf via an anonymous proxy. The problem is all the free ones are incredibly slow to surf via and are often run by hackers and identity thieves anyway (who will also log your data and use it!)
So these are the main areas you need to cover for complete anonymous web surfing, there are a couple more like search engine records but you're mostly protected by the encryption component.
You can cover all these components for free if you have reasonable technical skills, the most common problem though is speed - open source proxies are available through TOR but they are slow and difficult to install.
If you can afford a few bucks subscription I'd recommend Identity Cloaker which will fully encrypt your connection and give you access to a huge network of high speed anonymous proxies. You will have the complete anonymous web surfing package and better still you'll surf at high speed.
Here's the link for a free anonymous web search engine