This is my interpretation based on my own understanding, you should read the new Privacy Policy and Terms of Service yourself as I might not be 100% correct :) I know this is a bit long, but I've tried to put it as simply as I can.
Google have completely re-written their Privacy Policy and their Terms of Service, but it seems that the changes mainly apply when you are signed in to your Google Account, so they may share information about your activities on one Google service / product (like your signed in Web History) with other Google services / products you have under the same account. See the FAQ http://www.google.com/policies/faq/
When you have a Google Account and you are signed in, the main purpose of the new policy seems to be so that they can tailor your experience across different products that you use under the same account in terms of the results, suggestions and information they show you (rather than for targeted advertising, unless you have specifically opted in).
They will not share this information across different Google accounts you may have, and you will still be able to control your preferences under Google Dashboard and Ads Preferences Manager after the updated Privacy Policy and TOS come into effect. They will also not share any personally identifiable information about you with any third parties without your consent, see http://www.google.com/policies/privacy/preview/#nosharing
Unless you have specifically opted in to your personal information being combined with DoubleClick cookie information in your Google Account, there does not appear to be any difference in the way they target advertising to people who are signed in and people who are not.
Google currently targets advertising based on your use of their services using cookies and other information which can identify your unique computer whether you are signed in or not, this is also applies to the updated Privacy Policy and TOS see http://www.google.com/goodtoknow/data-on-google/advertising/
They also store search logs connected to your IP address and cookies stored on your computer whether you are signed in or not, but that also applies under current Privacy Policy and TOS and also the new versions, you can see the details about search logs here http://www.google.com/goodtoknow/data-on-google/search-logs/ Your IP address is anonymized after 9 months and the cookie ID will be replaced after 18 months. This is not much different to Bing which keeps similar data for 6 months and 18 months respectively http://privacy.microsoft.com/en-us/bing.mspx#EDB
Personally, I think people are over reacting a little, but if you are still concerned you can install things like Adblock Plus to stop adverts http://adblockplus.org/en/ , and use Do Not Track for Firefox https://support.mozilla.org/en-US/kb/how-do-i-turn-do-not-track-feature or Keep My Opt-Outs for Chrome https://chrome.google.com/webstore/detail/hhnjdplhmcnkiecampfdgfjilccfpfoe