I'm not as worried about sneaky things on the client side as I am about what they're up-front about. The URL bar sending everything I type upstream, for example. And I can turn my phone off any time I might be worried, in much the same way I can avoid using Chrome when I might not want to give Google data, which happens to be always.
To sort of explain, the whole concept of "privacy" as Google sees it is a little creepy to me. I realize that I may be overly cautious or paranoid, but I don't see any comforting counter-examples. I got rid of my Android phone on discovering that I couldn't have contacts or calendar entries that didn't get sent to Google in one form or another, and the Google Maps application wanted me to agree to allow location data* to be sent upstream even when I wasn't using it. Eric thinks we should just change our names. None of this sits well with me at all.
Even if they have no intentions of misusing data (which is stretching it), what they retain is still subject to subpoenas, leaks, hacks, or willful violations like Google Buzz (arguably unintentional) or the case of their SRE David Barksdale. Three people can keep a secret if two of them are dead, etc., and machines and the people who operate them have not had a good track record on safeguarding other people's data.
* The application did specify that the data collected would be "anonymous", but didn't say how that was ensured. Between Google's skirmishes with the EU over how they "anonymize" their search logs (spoiler: they don't, last I checked; they keep the cookie-tracking data and scrub the last octet of the IP) and their recent privacy issues with two different SREs don't inspire any confidence.