Google now provide an open DNS service. At first I was scared that they use their service to get information about users.
However, their privacy statement tells us that no personal identifiable information is stored for longer than 48 hours. The permanent logs do not contain such information. The most notable information that is stored permanently is the requested domain. The other thing is that they record the location of the request on the city level. And even that info is only stored for two weeks. After that, only a small random sample of info is stored for permanent storage.
The main question is now: who do you trust more: Google or your ISP.