If you are really uncomfortable never sign into any web service, they all do what Google is doing and a lot more.
If you really want to be sure no one is watching, use “Incognito” in Chrome or “Private Browsing” in Firefox. There will be no history and no tracking cookies. There will be no functionality as well!
Do you know who really knows about you? Your Internet Service Provider! Your ISP knows about everything you do on the Internet except encrypted sites (sites using HTTPS) like your bank or Gmail.