You must have heard about New Internet Explorer 8 or Google Chrome Browser and Private browsing mode they offer. Both of these browser have Private browsing mode (also called anonymous browsing). After reading about this you must be thinking you finally have some inbuilt tool but are they really providing same thing what you thinking ? I believe this term is misleading as it is something different than what private browsing really means.
I am not saying what they say is incorrect but you must understand correctly what and how this mode works, and what privacy will you get with these modes. The privacy mode offered by these or any other browser is not making you anonymous for private browsing which will not tell web server about you, But it will not leave any traces of your browsing history on the computer you using.
When You enable Privacy mode and start browsing, the browser will make sure that all your History, cookies and temporary files are deleted as soon as you close the browser. No one else using same PC will be able to find out what you did on that PC unless he have some other key logger or Action logger software installed. This is good for those who uses shared PC and often forget to logout before leaving the PC. In this case simply close the browser window and all your history and cookies deleted so nobody will be able to access your account even if you leave it signed-in.
Do you think this is what you looking for as far as privacy is concerned, If yes then these modes in the browser are designed for you and you found what you looking for. But you should know that whatever you doing on that PC is still recorded on the servers you visiting. So it is not pure anonymity for your action. Your private data which you shared with sites during privacy mode enabled browsing is still lying with servers which you accessed. SO beware of this mode and make sure you have all the tools you need.