The bottom part of the ZDnet article has a bunch of quotes from the EFF and EPIC leadership clamoring for some search engine to not keep logs, and general complaints about the ability of web sites to datamine their transaction history.
I don't think it's likely or realistic for a search engine not to keep logs, though maybe AOL could give up on improving user experience, fire ALL of their researchers and outsource all the privacy problems to Google.
Even if Google wanted to, Sarbox regulations require much more mundane business material to be kept for long periods of time, and certainly could apply to web server logs in Google's case. Beyond that, how would Google continue to improve their service, or continue to reduce click fraud if they didn't keep logs?
Here's the simple answer if you're that worried about privacy online: Don't use the Internet. Also, don't use credit cards, don't go to the ATM machine, don't have a driver's license, don't own a home, etc.
I'll be far more worried if the government steps in and decides to tell Google what they can or cannot do with the data they collect. If it happens, it will be more evidence that the tech industry under-spends on lobbying.