Ed Foster has discovered that it is very difficult to sign out from big companies’ websites. Yes, it is true when staying within the website’s rules. But it is dead easy otherwise.
The important thing to remember is that your identity is most of the times stored in the browser cookies. So, if you kill cookies, the session will go away and your identity will go away.
The easiest (but most destructive way) is to delete all cookies. With Firefox, this is the menu item Tools/Clear Private Data (Control-Shift-Del); on Internet Explorer 6, it is Tools/Internet Options/General/Delete Cookies.
The problem of course is that it all your login information for all the websites. Of course, if you were shopping on a public computer, that’s the best course of action anyway.
With Firefox, there is a much more precise way to delete the cookies. It comes with the Web Developer Extension - and cookie management is just one of that extension’s invaluable options. Once the extension is installed, it shows up as a toolbar. Cookies is a submenu on the left with a whole host of different options.
Using the extension, the easiest way to delete cookies is then to go Cookies/Delete Domain Cookies while on the target (Amazon, eBay, etc) website. This will delete all cookies set by that site and on the page refresh you will be a totally anonymous customer.
Advanced user’s notes
The above works in nearly all cases. Some websites get a bit sneaky and set Flash cookies instead. This is mostly done by websites such as YouTube, but for some reason images.amazon.com sets one as well. Deleting those can be done via Adobe’s Flash Player Settings Manager, which is actually a web page with specialised Flash application that shows cookies and allows to clear them.
Finally, deleting the cookie does not mean the website cannot track you otherwise. Google for example, will apparently use your IP address to correlate searches even across multiple sessions. It is not the same issue as keeping you logged-in, so I am only mentioning it in the wider privacy context.