Most browsers save your browsing history unless you are running them in a specific mode that prevents this. Chrome calls it 'Incognito' mode, and IE calls it 'InPrivate' browsing. These modes prevent stuff from being saved in the local (on your computer) browse history. This is not affected by what Google is doing and not really the point of this thread. What Google is starting to do is basically save all or your searches (which they have always done but anonymously) and tie them to your specific Google log in. So if you use Gmail, Google will now keep a history of searches performed by you tied to your user account. As an example, Google would previously know that 8 million people searched for 'Blueberry Pie' (but anonymously). Now, they will know and track that
JoeBlow@gmail.com searched for 'Blueberry Pie on my escorts breasts.' Since they are now storing and tracking individual users' search histories, these records can be subpoena'd with a court order and used against you. Now, I will admit, it's fairly unlikely that LE would go to the trouble of doing this. It's really more of a privacy issue. Google, not just your web browser, is tracking all of your searches and can tie them back directly to you based on your Google login.