I have recently started using the WhiteHat Aviator browser, which uses the anonymous search engine Disconnect. It is available for Windows and Mac here. It works pretty well (although it is sometimes slow). When I use it for sites like Gmail where I use two-factor authentication, I do have to enter both the second factor and the password every time I load the website. It will not save the code like Firefox can for thirty days.
I am planning on installing Disconnect on my phone next. If that works out, I will try the premium version, which includes encrypted Internet, safe browsing, and location control.
Another anonymous search engine is DuckDuckGo.
I also use Firefox with extensions NoScript, Ghostery, Adblock Plus, and Lightbeam. Lightbeam is particularly fascinating to look at; it shows all the sites that track me, even after all those add-ons. NoScript can be painful to use because you have to enable every single site.
After the last set of Adobe Flash 0days (two in a week!), I uninstalled Adobe Flash and Air. After all, if I really need Flash, I can always use Google Chrome, where Flash is built in.
I rarely use Internet Explorer any more.
And while you are updating your browser, make sure your Java version is current.
Intentional Privacy 