Even if you have a static IP, only your ISP would know WHO you are, unless you have a registered domain name under that IP.
But, even with a dialup account and non static IP, it's possible to know almost exactly WHERE you live. Blocks of IP's can be tied to geographical locations, depending on the ISP.
I use Bell South, and my log-in cookie has a term "gloc=xyz" where xyz is the city I live in. I get (unwanted) targeted 'dating' ads because of that, and because of the Bell South practice of assigning IP's based on where the account is. Bell South is selling that info to people who target ads based on geography. I can delete my cookies, but the only way to truly hide my IP is through a proxy server.
If I use anonymouse's German http proxy and visit certain web sites, the dating ads will have German cities and German women. And, no they don't look any better over there. [Set phasers to shave, Mister Sulu].
If Google is forced to surrender search record logs, and those logs have IP's with them (they probably do) and your ISP keeps logs that far back and the gov't demands that log, then you've been made. If you use AOL, then probably not, because AOL intentionally mucks up IP's internally, for members privacy and to limit hacking of members computers. If you use anonymouse for your Google searches, then definitely not,either.
I have a Yahoo account and they will sell personal info if you let them. iccintelliserv.net cookies are the ones they are using to pass off where you go. Block cookies from that domain and they have a harder time spying on you.
Since browser helper objects in IE have the same process ID as the browser it's almost impossible to prevent Windoze from calling home if you go on the net in IE.