"We built Google Public DNS to make the web faster and to retain as little information about usage as we could, while still being able to detect and fix problems. Google Public DNS does not permanently store personally identifiable information."
What other expectations for a DNS server do you have? If you do a lookup for example.com's A record, it's going to know that someone looked up the A record for example.com.
As I mention in a related comment, if you're worried about the NSA knowing what websites you visit, you must not use TCP/IP. TCP/IP has no provision for obscuring the source and destination of packets; you have to add that at another layer.
(To wax philosophical, it seems that we're outgrowing the Internet. Nobody was worried about protecting their browsing history from their ISP or the government when the Internet was designed, so when we start talking about "if you use XXX service, the NSA can find out", that's true of pretty much everything except for things specially designed to hide browsing history from the NSA. Even those can be suspected to be compromised, meaning you shouldn't even be here commenting if you're truly worried about what information a DNS server might collect from you.)
"We built Google Public DNS to make the web faster and to retain as little information about usage as we could, while still being able to detect and fix problems. Google Public DNS does not permanently store personally identifiable information."