I agree that using Buzz is as bad an idea as using Facebook, or any social networking service, and that everyone should please follow the guidance posted above to avoid compromising his own, or anyone else's privacy/anonymity.
That said, it seems that Google has been listening carefully to all the complaints they've been getting, and are working on fixing the privacy concerns. Here is what they posted today:
A new Buzz start-up experience based on your feedback
Saturday, February 13, 2010 3:53 PM
Posted by Todd Jackson, Product Manager, Gmail and Google Buzz
We've heard your feedback loud and clear, and since we launched Google Buzz four days ago, we've been working around the clock to address the concerns you've raised. Today, we wanted to let you know about a number of changes we'll be making over the next few days based on all the feedback we've received.
First, auto-following. With Google Buzz, we wanted to make the getting started experience as quick and easy as possible, so that you wouldn't have to manually peck out your social network from scratch. However, many people just wanted to check out Buzz and see if it would be useful to them, and were not happy that they were already set up to follow people. This created a great deal of concern and led people to think that Buzz had automatically displayed the people they were following to the world before they created a profile.
On Thursday, after hearing that people thought the checkbox for choosing not to display this information publicly was too hard to find, we made this option more prominent. But that was clearly not enough. So starting this week, instead of an auto-follow model in which Buzz automatically sets you up to follow the people you email and chat with most, we're moving to an auto-suggest model. You won't be set up to follow anyone until you have reviewed the suggestions and clicked "Follow selected people and start using Buzz."
For the tens of millions of you who have already started using Buzz, over the next couple weeks we'll be showing you a similar version of this new start-up experience to give you a second chance to review and confirm the people you're following. If you want to review this list now, just go to the Buzz tab, click "Following XX people" and unfollow anyone you wish. If you don't want to share the lists of people who are following you and people you are following publicly on your profile, you can opt out at any time from the edit profile page.
Second, Buzz will no longer connect your public Picasa Web Albums and Google Reader shared items automatically. Just to be clear: Buzz only automatically connected content that was already public, so if you had previously shared photos in an "Unlisted" album or set your Google Reader shared items as "Protected," no one except the people you'd explicitly allowed to see your stuff has been able to see it. But due to your feedback Buzz will no longer connect these sites automatically.
Third, we're adding a Buzz tab to Gmail Settings. From there, you'll be able to hide Buzz from Gmail or disable it completely. In addition, there will be a link to these settings from the initial start-up page so you can easily decide from the get go that you don't want to use Buzz at all.
It's been an exciting and challenging week for the Buzz team. We've been getting feedback via the Gmail help forums and emails from friends and family, and we've also been able to do something new: read the buzz about Buzz itself. We quickly realized that we didn't get everything quite right. We're very sorry for the concern we've caused and have been working hard ever since to improve things based on your feedback. We'll continue to do so.