If you're using a Google Profile - which describes anyone using the new Google+ social network - Google's issuing an ultimatum: If you don't make your profile public by July 31st, Google will delete it.
Here's Google's official help article on "Public Profiles:"
The purpose of Google Profiles is to enable you to manage your online identity. Today, nearly all Google Profiles are public. We believe that using Google Profiles to help people find and connect with you online is how the product is best used. Private profiles don’t allow this, so we have decided to require all profiles to be public.
Keep in mind that your full name and gender are the only required information that will be displayed on your profile; you’ll be able to edit or remove any other information that you don’t want to share.
If you currently have a private profile but you do not wish to make your profile public, you can delete your profile. Or, you can simply do nothing. All private profiles will be deleted after July 31, 2011.
In other words, if you've been keeping your Google Profile private for the sake of social media invisibility, well - you can't. Google is requiring that Google+ users be able to at least see that you exist on the network when doing searches. Oddly enough, Facebook still allows users to pull a more complete disappearing actthrough a judicious use of privacy settings.
As Searchengineland points out, though, Google Profiles do still have the option to avoid Google search indexing. But anyone within Google+ can still track you down thanks to this change.
It's obviously part of a play to help the fledgling Google+ Project get off the ground - more public Google Profiles searchable means more connections made means more active users. What's more is that I don't think most people will even notice the change.