History Block Firefox add-on allows users to create a list of URL that will not be logged in the browser's records--history tab, recently closed tab and download manager. If I have opted to keep Google out of browser's memory (Google is innocuous? Really),whenever I search for something on Google, it won't be recorded by the browser, though other sites that I visit after clicking on search results will be logged in. However, History Block may divulge the secret by letting others see the cookies saved during your adventure trip.

If you wan't a complete secrecy of your Web browsing, try Stealther firefox add-on. It adds a stealth mode to the Web browser, quite similar to that availabel in Google Chrome. Turn on stealth mode, and jump from on site to another without worrying about someone getting to know what sites you visited.

To make change to Stealther settings, go to Tools->Add-ons->Extensions and click on "Preferences" tab next to Stealther. To turn on Stealther, use the short-key or go to "Tools" menu and select Stealther option. You can also get Stealther in status bar.