I have added a screenshot of firebug console in firefox (press F12 to open it). I executed a xmlhttprequest (line at the bottom) and you can see (the black line) that it connected to stackoverflow. Firebug shows xhr connections in the console by default but you can select what you want to see by clicking the little arrow button to the right of the word "Console" in the tab that activates the console.
Even having the console open with StackOverflow shows that the site connects every so often to update question status and comments.
If nothing shows up there than it might show in the Net tab. It has to make a connection to somewhere to see if network is still up. If it connects to a service than xhr is likely if it just tries to download a textfile sometmes or sets the src of an image than it'll show up only in the net tab every time it checks.