Application Network Auditing
I see that many people carelessly express their opinions about how private and privacy oriented some applications are, especially in the browsers landscape, but, so far, all failed to report a strict analysis with real world data or numbers.
Here you can find some of the possible ways of auditing a web browser for background network connections. Specifically to see if it phones home, if it bypasses the system dns, if it contacts third parties.
While this type of auditing requires some experience in networking, it is also meant to be naive and superficial by showing only connections and not their content, to show what actually happens behind the scenes and finally have some actual real world data and visuals on this.
There are easier or quicker ways of doing this kind of test, for these, check the last part of this article where I propose some alternative methods.