If you don't want Google to track you will have to log out of your Google account and ensure that cookies are switched off in your browser preferences as well. But, if you're logged out of your Google account than most of their services are useless (i.e., Gmail, Google+, Calendar...) so that's not really an option if you use them constantly, as I do. Now this is quite a big change for Google because until now each service has acted as an island. If I schedule a meeting in New York for next week in Calendar I would not expect to see adverts for NY hotels appear in my Gmail. After March 1 that is exactly what you can expect to happen; this is the "more intuitive Google experience" to which they refer.
Of course from Google's perspective aggregating and analyzing all your online activity will greatly enhance their ability to target advertising at you. They will be privy to your personal and professional life, your diary, email, documents, viewing habits, everything. If they can successfully mine this data (and if Google can't nobody can) then they should be able to target adverts with greater precision than anyone ever thought possible.
Will there be a public backlash? I doubt it, most people will just shrug their shoulders and think "I've nothing to hide." I for one though would sleep easier if Google were based in Sweden or a similar liberal social democracy. Imagine how much information the US government will be able to get on an individual if they subpoena Google for their records, which have now conveniently been aggregated into one place.
You can read Google's press release here or watch the video below.