Jetée

You can always not log in to the search engine in which you are using. That way, no trail, no name, no history (save for the cookies from your browser, but those can be cleared out easily).

Also, as AquaFox mentioned, near at all costs, do not use any traces in daily web activities that make mention of who you "actually" are, whether that be your name, where you live, or what sort of personal communtiy you belong to (married, college-life, working at Home Depot). This is an extreme approach, of course, but this is the optimal solution for the extremely paranoid, average net citizen.

I'm not sure of their validity, or how much they work to throw someone like the CIA of your trail, (if they, indeed, were ever on it to begin with) but try using web anonymizers, or what do you call them, "something-IP"? I don't know how they work exactly (save for the fact that I bought one which claims to allow me to appear like a 'static, stationary user') but I think they work similarly to how a website admin views a person who acesses their site via Google's cache. They don't know from where it came from precisely, as it is Google's snapshot of what it appeared like from it's crawler's last visit. I could be totally wrong on that example, though.

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As human beings, our greatness lies not so much in being able to remake the world (that is the myth of the Atomic Age) as in being able to remake ourselves.

—Mohandas K. Gandhi