A lot of people are worried about the privacy implications of using Google's DNS resolver. Paranoia is good, but it's probably overblown here. As far as I know, the primary objective of the project is to provide a fast, accurate DNS resolver, not to collect data. So much so that when it launched, it was originally called 'Honest DNS', as you can see on this bizarre Twitter account: https://twitter.com/honestdns
edit: Also of interest, Google does disclose exactly what data is logged, for the paranoid and curious: https://developers.google.com/speed/public-dns/privacy
(Disclaimer: I work for Google, but not on this. All of my knowledge of this service comes from being an end user, on the outside. Hopefully I didn't mess up any of the details.)