Almost any distro I know connects to the internet to get the latest updates of software that's installed. Even if you're performing a 'fresh' install from a recently downloaded iso, there might be packages that are already in need of an update, be it for security update, bug fix or whatever.
Most of the distros leave that control to the user but in Ubuntu and other *buntus the system takes care of that automatically. I'm sure there is a way to turn the automatic updating off but don't know where it's configured (I'm not a frequent *buntu user).
The feature is by default available on all installations of Linux distros that I came across, albeit with the difference that some of them connect and update (semi)-automatically and other are launched manually by the admin. I have Debian servers running and none of them connect by default (that is after installation is completed from netinstall). They all wait for my command to update / upgrade. Same goes for Slackware on my home laptop.
Hope this helps out a bit.