All the data Google automatically gathers about you, such as the sites you visit, will be dumped into one virtual bucket with your name on it. While you can't opt out of the new approach without abandoning Google sites, you can erase your browsing history.
The Electronic Frontier Foundation (EFF) recommends deleting your Google web history, as it can reveal sensitive information about you such as location, interests, and much more. They even go as far as giving you directions on deleting it:
Go to Google.com and sign into your account.
Use the dropdown menu under your name in the upper right-hand corner to access your settings. You'll now be on your accounts overview page.
Find the section called Services and you'll see a link to "View, enable, or disable web history." Here you can remove all of your Web history or selected items. When you disable Web History it will remain turned off until you turn it back on.
While this doesn't stop google from collecting data, it does make this data anonymous. Your search results may become less personal and "focused", but that seems to be a small price to pay for not having your private information out on the web to see.
Do you have a google account? Are you planning on deleting your Google web history? If you are, don't delay, as March 1st is only a day away.