If you don't want other people to know what you read, you probably shouldn't own an ereader. And you really shouldn't get a constantly connected Kindle or Nook, at least according to the EFF's eye-opening guide to ebook privacy.
The Kindle and Nook are tied to Amazon and Barnes & Noble's respective bookstores, meaning every purchase and every book search is recorded. Amazon's license agreement for the Kindle, for instance, notes that the Kindle's software "will provide Amazon with data about your Device and its interaction with the Service...and information related to the content on your Device and your use of it (such as automatic bookmarking of the last page read and content deletions from the Device)."
The Nook is obviously capable of phoning home in a similar manner, but it's unknown whether or not it does, at least for now. With Google Books, it's clear that what you're actually reading is logged, down to the specific page.
On the other hand, since Sony's Reader lacks 3G for a constant connection and isn't as tightly integrated with their ebook store, there's less opportunity for data collection, particularly if you stick w/ sideloaded books. Better still, says the EFF is the open-source FBReader. But you can't download books from anywhere in 3 seconds over 3G, and the experience isn't as nice.
It's the classic tradeoff: Less privacy for more convenience and a better experience, or greater privacy for a bigger hassle. What side are you on? [EFF]