DuckDuckGo
OK, DuckDuckGo isn’t really browser, it’s a search engine. If privacy is a concern, adding a DuckDuckGo search widget to your default browser can change your Internet experience dramatically.
To compete with Google and Microsoft, DuckDuckGo has made user privacy its number one concern. A DuckDuckGo search leaves no browser history or trail of any kind.
PROS: You can’t beat DuckDuckGo’s straightforward attitude towards privacy. That means your, totally legitimate, interest in Twilight fan fiction is no one’s business but your own.
CONS: Obviously this search engine is off the Google grid and of limited value for SEO purposes. (Though plenty of affiliate partners might not see that as such a bad thing.)