Pick whatever search engine you want - your privacy is still out the window. In case anyone isn't aware - whatever site you end up at can see what search terms you used to get to that site. It shows up as referral link and they see exactly what keywords led you to their site in a list on their tracker. Anonymously, of course - but it is recorded in their logs. Also, if you are on another site and click a link to get a different page, that new page will see what link you clicked to get their site.
Also, good chance whatever site you end up at will throw you a google cookie that follows you at least until the end of your browser session. It is pretty much necessary to use the Internet at all. Look at your cookie list right now - there will likely be a huge list there unless you fastidiously keep an eye on it. Google owns doubleclick, which the ad server used by a large portion of the Internet, in addition to their own ad service.
You can turn off cookies completely but then you can't login in anywhere , and it makes doing anything at really cumbersome. I use NoScript and Adblock, and I can't even remember the last time I saw an ad on the Internet when using Firefox. I also clear cookies when I close a browser window.
Even without seeing Google ads (the ad server can still be blocked with NoScript) the cookie ends up there when you use Youtube or end up on a site where you have to turn on some combination of scripts to load the page at all when their developers get tricky and try to display ads to people with blockers. I can't imagine what trying to use the Internet without Google is like. Oh wait - yes I can. 1995 and using Yahoo.
Privacy is gone, folks - I don't mean it in a paranoid way, just an accepting one. I welcome my Google overloads. (just please stop sharing info with the NSA, ok? thanks)