IMO some danger comes from Google, or perhaps a future version of Google; however a real danger that exists right now is that Google's data is used by the US government in a manner that breaks constitutional protections.
I do agree that there is much convenience to be had, but we could have the same, if we started with the assumption that users did not want their behavior logged, but that they could opt into it. The current standard with Google is that if you have a Google Account, then you agree to what data they harvest. Imagine if Comcast said that if you use their service, they can similarly harvest your data. Where I live, my internet options are limited to AT&T or Comcast. If they both had the same conditions, I would have no choice for an internet that doesn't record my behavior.