Do you know about this development as described in this article in Slate.com? Google will now allow your gmail e-mails to show up in searches. What's more, like the Book of Face, they don't give a rat's ass is you like it or not. Searching and gmail are their toys and they will do what they want with them. You just have to suck it up.
Maybe I misunderstand the extent of this story, or some of the finer details about Google's implementations; but this sounds to me as if your gmail e-mail becomes public whenever you log on. The ability for Google to return your emails in a search, seems analogous to the Post Office opening your mail and posting bits on a bulletin board. That is probably a naive analogy, given that nothing at all is private once you log onto the internet. Nonetheless, don't you have a password because you expect a modicum of control over the eyes on your e-mails? That expectation is naive, too.
I have a gmail account, which I opened to use as a work account between jobs and will use as professional account for non-school business because I seem to change institutional affiliations frequently and who knows what might happen in the future. Things that become portable, like professional memberships, go with that account. I also have an ancient Yahoo account for personal business. So, even under my own name, I try to keep the personal and the professional separate. The problem comes with other people, regardless of age, who don't understand the need and even resent the necessity of having some distinctions between the two. I have also used the Yahoo account to contact people about "off the record" work things, but now I wonder if Yahoo will end up in the same place as gmail in search engines.
Perhaps a bit more disturbing is that the school uses gmail as its own e-mail -- what would you call it? server? service? In any case, you essentially use gmail to log into your work e-mail. Of course, I have long since learned that your employer claims a right to all e-mails generated on that account, I have been careful of the ways that I use it and what I say on it. Nevertheless, this adds another layer to your employer's ability to crawl through your communication.
[ETA] Also, it seems as if there are some legal privacy questions here, too, such as communications between students and professors. Exchanges about grades in particular would fall under FERPA, so the school probably should have some sort of security or exemption from e-mails appearing in searches.
Entering the internet seems to have become more and more like entering a panopticon. At the same time, speech on the internet seems to have become less and less free (see the ruling that a Book of Face "like" is not protected speech). Paranoia to the point of opting out as much as you can is probably healthy when you have to be vigilant over even the smallest interaction online.
Oh, and even receipts? Really? I suppose the Google people all know how to protect their own online accounts, but would they seriously want some of their online purchases appearing in a search engine? That could be pretty embarrassing!