Those of us concerned with our anonymity and privacy on the Internet cannot help being worried by the recent developments. First, there were the infamous Windows 10 issues, then came the resurrection of the old debate about the cyber-warfare and all the things that go together with it. Not even phones are safe from prying eyes these days. it seems that our only choice is to gear up and find a way to go online unnoticed. Luckily, there are tools to help us.
Tor Browser
The famous (or infamous) Tor browser is probably the first tool that you think of when private browsing is mentioned. It's a crafty tool for avoiding the standard traps of deanonymization. It uses special servers and data re-routing to keep your personal data from falling into the hands of people who might want to track you.
Of course, this method is not perfect and may impact stability and functionality of the browser, but if it's anonymity you want, then this is the best choice. If you hande it right, Tor will make you practically invisible on the Web.
Tor is based on Firefox, but has only a fraction of its functionality, since remaining anonymous means turning off most of the plugins and extensions. However, easy free access and a variety of versions make up for it. It's important to remember that this browser keeps you anonymous, but does not encrypt your data, so the protection you may want is possibly different from what Tor can give. See this guide to see if this browser can be of use to you.
Epic Privacy browser
This browser is based on the Chromium technology and will seem pretty similar to Chrome. Unlike Tor, Epic Privacy is capable of much more than making you anonymous. It blocks all possible kinds of ads and widgets, prevents online services from tracking cookies, controls downloads and scripts. It even has what Tor is lacking - encryption with HTTPS / SSL and re-routing via proxy servers. Protection during the use of public Wi-Fi is also a nice addition.
I don't know about epic, but it sure is private...
Epic Privacy doesn't support standard Chrome plugins, but works significantly faster and is much easier to install. It's currently being developed in terms of stability, but can already provide a good means of browsing the Web while keeping your privacy. The only thing I found a bit annoying is the inability to save browsing history, passwords,and other things that would make it a much more comfortable bowser for everyday use. So, the best option is to use it as a special tool for special cases. Luckily, it works pretty well as a secondary browser. I recommend using Chrome for regular browsing and switching to Epic Privacy when you need it.
Comodo Dragon/Ice Dragon
These twin browsers are included together because they are basically two variations of the same solution based on different platforms.
The Comodo Twins - sounds like an action movie title
Comodo Dragon is one of the first Comodo browsers. It is based on Chromium and has the standard set of tools like the double-checking of the company that issued your SSL certificate and traffic routing using protected DNS. The browser also keeps track of your cookies, widgets and other site components for possible harmful or suspicious elements that can try and access your private data.
Ice Dragon is based on Firefox and is much more comfortable if you usually use Mozilla's product. The level of protection is basically the same as in Comodo Dragon, but this version supports third-party extensions. It can also scan pages and sites to identify dangerous elements as soon as those start loading and issue a timely warning.
The Comodo browsers were not originally made with anonymity in mind, but their tools and features naturally became useful in maintaining your incognito, at least partially.
Other
There are various other browsers that boast privacy and security. However, I urge you not to use them. Most of those browsers are either illegal variations of regular browsers, like the anonymous version of Opera, or simply lack the real functionality to actually make your online activity anonymous, like the Pirate Browser. There are also some browsers based on Chromium that promise privacy protection similar to Epic Privacy, but unlike it, they are not proven to be functional, reliable or even open source, which is basically a must for a browser trying to appeal to the general user.
Therefore, I ask you to be very careful about what tool you use to keep yourself hidden. It's always better to be a little more tech-savvy and learn a few things about encrypting data or turning your Windows 10 account into a local one, or even pressure big companies to do something about the current lack of privacy. Either way, the best weapon of a private person is awareness.