Yes. Google, MSN Search, Yahoo, AOL, and most other search engines collect and store records of your search queries. If these records are revealed to others, they can be embarrassing or even cause great harm. Would you want strangers to see searches that reference your online reading habits, medical history, finances, sexual orientation, or political affiliation? 
The FBI is pressing Internet service providers to record which websites customers visit and retain those logs for two years, a requirement that law enforcement believes could help it in investigations of child pornography and other serious crimes.
FBI Director Robert Mueller supports storing Internet users’ ‘origin and destination information,’ a bureau attorney said at a federal task force meeting in February 2010. As far back as a 2006 speech, Mueller had called for data retention on the part of Internet providers, and emphasized the point two years later when explicitly asking Congress to enact a law making it mandatory. But it had not been clear before that the FBI was asking companies to begin to keep logs of what web sites are visited.
The FBI is not alone in renewing its push for data retention. As CNET reported in February 2010, a survey of state computer crime investigators found them to be nearly unanimous in supporting the idea. Matt Dunn, an Immigration and Customs Enforcement agent in the Department of Homeland Security, also expressed support for the idea during the task force meeting.
Greg Motta, chief of the FBI’s digital evidence section, said it was trying to preserve its existing ability to conduct criminal investigations. Federal regulations in place since at least 1986 require phone companies that offer toll service to ‘retain for a period of 18 months’ records including ‘the name, address, and telephone number of the caller, telephone number called, date, time and length of the call.’ 
Google voluntarily complied with the FBI request and keeps track of every web site you visit if you use its browser. Anyone who uses Google Chrome web browser can go to the Google web site and look up their surfing history. 
Google admits that it keeps track of what books you read on Google Books, but claims it keeps the information for a ‘limited period of time to enforce viewing limits.’ 
Google and Microsoft admit they keep track of every search users make.  Let Google speak for itself:
Why does Google store search engine logs data?
We store this data for a number of reasons. Most importantly, we store data to improve our search results and to maintain the security of our systems. Analyzing logs data helps our engineers both improve your search quality and build helpful innovative services. Take the example of Google Spell Checker. Google’s spell checking software automatically looks at a user’s query and checks to see if that user is using the most common version of the word’s spelling. If we calculate a user is likely to get more relevant search results with an alternative spelling, we’ll ask ‘Did you mean: (more common spelling)?’ In order to provide this service, we study the data in our logs. Logs data also helps us improve our search results. If we know that users are clicking on the #1 result, we know we’re probably doing something right, and if they’re hitting next page or reformulating their query, we’re probably doing something wrong. In addition, logs data helps us prevent against fraud and other abuses, like phishing, scripting attacks, and spam, including query click spam and ads click spam.
Why are search engine logs kept before being anonymized?
We strike a reasonable balance between the competing pressures we face, such as the privacy of our users, the security of our systems and the need for innovation. We believe anonymizing IP addresses after 9 months and cookies in our search engine logs after 18 months strikes the right balance. 
Google is an intricate part of Big Brother. It keeps all data forever. Google and other search engine providers keep track of your searches and create a profile which it sells to advertisers. Google makes millions of Federal Reserve notes doing this, but it also gives Big Brother this information. It dutifully turns over information upon request from governments. 
 ‘Six Tips to Protect Your Search Privacy.’ Electronic Frontier Foundation. September 2006. www.eff.org/wp/six-tips-protect-your-search-privacy.
 McCullagh, Declan. ‘FBI wants records kept of Websites visited.’ Cnet.com. 2.05.2010. http://news.cnet.com/8301-13578_3-10448060-38.html.
 www.lifehack.org/articles/productivity/track-internet-history-on-any-comput er.html.  http://books.google.com/support/bin/answer.py?hl=en&answer=43733.
 http://forums.canadiancontent.net/computers-internet/80817-did-you-know-mi crosoft-google.html.
. Marco, Meg. ‘Microsoft Developing Software That Can ID You From Your Browsing Habits.’ Consumerist. 5.23.2007. http://consumerist.com/2007/05/micro soft-developing-software-that-can-id-you-from-your-browsing-habits.html