Using Gnome Shell, how do I get rid of the Network icon from the top right in the panel?
I would suggest using the Evil Status Icon Forever extension. Install it by clicking the On toggle switch HERE and open and edit the extension.js once installed:
gnomesu gedit ~/.local/share/gnome-shell/extensions/EvilStatusIconForever\@bone.twbbs.org.tw/extension.js
You then change the section below by uncommenting what you'd like to hide, in your case "network" so it would look like so:
var removeStatusIcon = [ // 'a11y', // Accessibility // 'volume', // 'battery', // 'keyboard', // 'bluetooth', 'network' ]
Ctrl+s to save.
Or you could
/etc/init.d/network-manager stop. That gets rid of it. To get it to stay gone, you could
mv /etc/init/network-manager.conf /etc/init/network-manager.conf.bak. Of course, if you're on a wireless connection you might have one heck of a time getting wireless running unless you set it up in /etc/network/interfaces.
l300lvl's answer is so much better