As of August 1st, Google will delete all private Google+ 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.
Like Facebook, Google will require the minimum of details to be public, namely your full name and gender. You can edit or remove any other information that you don’t want to share.

Don't want that info public? If y you leave your Google+ profile private, Google will simply delete it after July 31, 2011.

From: https://www.google.com/support/profiles/bin/answer.py?hlrm=en&answer=1192471