A lot of people I know use DuckDuckGo.comhttps://duckduckgo.com/privacy
That link doesn't just show their privacy policies, but it also has articles on there showing how tracking on search engines works, how the popular search engines tailor results to you specifically (more tracking) and how you can change settings in your browser to help curb some of the techniques that are used. Even if you don't wind up using DDG, I think the information they provide is worth the visit. DDG will also search sites directly for you. You can search for Bikinis on Google Image search by typing !i Bikini. That's an image search for bikini. There are a lot of other sites that can be searched. Using !wa lets you type in formulas for Wolfram Alpha to solve. Here's a link to a more comprehensive list - https://duckduckgo.com/bang
Both of the above come highly recommended by those that are interested in protecting their identity. Each one will provide you with different search results, so I suggest giving them a try and seeing which you prefer. Though for the ultimate privacy in searching the web, you would need to self-host an engine such as Searx ( http://tuxdiary.com/2014/12/22/searx/
). Generally, crawling the web is incredibly time consuming for a Desktop and the results aren't optimized the way a typical user would expect them to be, but as you are in control of them, self hosted engines are the best for privacy, and if you are willing put in the time you can edit the output to fit your requirements.
Hope this has helped.