Can you surf the web anonymously?

Since I am into computer security and hacking, I am really concerned about anonymity on the internet. There is so much information you are giving away when browsing to a web site.
I personally do not think that you can surf the web anonymously. There are too many factors which you have to account for before being able to browse safely. But I am working on reducing these factors. I am thinking of creating a Firefox extension which helps you protect your privacy and anonymity. And I know there are already a lot of them out there but I do not think that they do a good job at protecting you, at least most of them.

So what do you think? Do you think it is possible to surf anonymously?