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It only works if you are logged in, so I guess you don't log in to Google if you don't want the two integrated. Although, now that I think about it, if you use Talk, Voice, Calendar, etc. then you pretty much have to be logged in all the time. I'm logged into Google right now, in fact, sitting at my desk at work. While I'm not too worried about girlfriends, here at my office it isn't uncommon to do a quick search on the nearest computer, and I don't really want information from my Gmail popping up when someone uses my computer to google something.
So, yeah, I'm with jimlynch on this; I hope that it is an opt-in thing.
First of all: hiding stuff from the current girlfriend about a past girlfriend? Never a good idea.
Second: Surely if you sign out of the Gmail account, your account info will no longer be included in the search results, right? So sign out of your account. IF you don't want the current girlfriend poking around your email, that is the best solution anyway.