10.1 automatically connects to ArcGIS Online without a possibility of turning it off, a "feature" many enterprise users would consider to be recklessly implemented. There has been an enhancement request logged to do this. In my case, this would create the appearance that I'm constantly on the internet for the internet monitoring software that IT is running and I could get written up. Also, people have noted the inability for 10.1 to pass security check analysis due to the additional network connectivity initiated by 10.1. In the meantime, I do the following to prevent it:
Use Internet Explorer 8, which allows you to work offline. Open the browser and set it to work offline (File - Work Offline), then close the browser to save the change. When you use the internet again, go to a page and you'll get a popup to work online again. Then, when you are done, switch it back to work offline. This won't work in IE 9, because any time something attempts to connect to the internet, even if you have it set to Work Offline, it will connect, assuming you wanted to. You can uninstall IE 9, which is a garbage browser anyway, hide it from updating in Windows update and just keep 8. Even if you use another browser as your main browser, you can still do this using IE 8 for the setting, or you may be able to go offline in another browser like Firefox. I don't know how other browsers handle that as I'm blocked from installing anything better or more secure here.
If someone else has a way of permanently disabling the connection, please share that here.