I find this article at the Economist unusually non-objective, and based on hearsay. Nonetheless, it represents how a growing number are feeling.
Google | Inside the Googleplex | Economist.com
Not everybody is impressed. The server logs will still exist for 18 months. And the cookies of “active” users will be automatically renewed upon expiry. This includes everybody who searches on Google, which in effect means most internet users. Then there is the matter of all that other information, such as e-mail and documents, that users might keep in Google’s “cloud”.
The concern about Google is overstated. Who worried about the Post Office opening their mail? The PO is regulated, some will say, but criminals within the PO, and Government Agencies with access to the PO didn’t worry about that.
Odd comparison you might say, but at the end of the day, someone has your data. Today it happens to be Google. Yes Google has my email, search history, spreadsheets, and documents. Does it matter?
What specifically are we worried about? Is the risk that you will see my documents or email, and if so, what is the real downside? Has that exposure of our information happened, and is it likely to happen? More importantly is it more likely to happen now than in previous times? Documents have been sent via email for over 10 years, and those documents sit in ISP servers all the time. Now that we have moved to web mail, no-one talks about that old risk.
No, at the end of the day, these are manageable risks, and the issue is probably not Google. The issue is more to do with “keep under the mattress” syndrome. Google might just be a manifestation of some deeper underlying fear.

I’m not at paranoid about Google. I use Google Search, Gmail, Gcal, and just about anything else they release. However, there is quite a difference in a company that handles communication you send (like mail or email or even phone calls) and one that collects the things you choose to read about.
Let’s look to the local newspaper as an example. In “the old days” if I only wanted to read articles about “Gardening” or “Needlepoint” that was done in the privacy and it was my choice as to whether I ever shared those preferences with others. (Not that’s there’s anything wrong with a 25 year old male that’s into Gardening and Needlepoint.)
Today, if I go online and read the same things, now someone else has the power to share those preferences, even profit from them.
To me it is worth giving up that bit of control in return for the vast amount of content available on the web. However, I do see it as a significant step in the realm of personal privacy.
Everyone needs to assess the risk of sharing the kinds of information that they share online and see the risk-return tradeoff (as Mark has done). Revealing less/ slightly inaccurate personal details on social networking/ other sites is one way, using anonymizers is another. There are ways of securing more important data online using encryption, but that has some problems…
Personal experience: I try to backup important emails by sending a copy to Gmail. In one such instance I had sent a password-protected (ok, encrypted) ZIP file containing details of my tax returns to my CA. He got the file on Yahoo mail, but Gmail bounced the copy mail with a message stating that encrypted ZIPs are not accepted. (This has been fixed now). Even more importantly, my organisation bans encrypted ZIP files from being emailed/ uploaded.
@Shreepad … for backups, I have been using Amazon S3. The tool that does this is Jungledisk. Every night, it automatically backs up my files, securely, to S3. When I got a new laptop earlier this year, all I did was restore the backed up directories to the new laptop and I was all set.
Costs me $2 per month +/- for 8 gigs +/-
http://www.amazon.com/gp/browse.html?node=16427261
http://jungledisk.com