The Tor Project promises anonymous web browsing as well as other subterfuge. "Tor" stands for The Onion Router. The simplest explanation of anonymous web browsing is to broadcast or state your current IP address as something other than what your ISP (Internet Service Provider) assigns to you.
Anonymous browsing is different than using Internet Explorer's InPrivate mode or Chrome's Incognito mode. Those browsing tools allow you to hide your browsing activity from your local hard drive. However, you're still browsing from a known location.
In other words, Comcast knows I'm a specific customer simply by looking at my IP address. It is how Comcast knows to allow you, for example, to download their Comcast-branded Norton Security Suite - which is equivalent to the retail consumer version of Norton 360 (not the Premiere version). It also allows your ISP to track your connection (for Comcast, the cable modem) to a physical address.
In other words, if I choose InPrivate or Incognito browsing, websites that I visit will still see my IP address as the same as regular browsing. It's like pinning a "Hello, My Name is ... and I live at ..." badge on my chest, wherever I go.
So perhaps you would want to hide who you are from the rest of the Internet. Tor will allow you to say that you're Johnny and you are at Johnny's house - although you don't get to pick which Johnny.
You can set this up with Tor's utilities and use Internet Explorer or Firefox or Chrome.
Tor can also be implemented via a USB stick.
I might test out Tor on a backup PC, but I'm not interested - I don't feel the need for anonymity, really - in anonymous browsing.
As the joke goes, I'd like to tell you something about paranoia, but not while you're looking at me like that.
Again, no judgements!