David McMahon posted this question on his blog (http://david-mcmahon.blogspot.com/2007/11/weekend-wandering_11.html) and I thought I would do my best to answer it.
One week without the internet would lead me to change many of my habits. On my way to and from work I listen to podcasts downloaded to my iPod. When I arrive at work I go into the office and check my emails. During the day I will often get students to look up some information or undertake a task on the internet. There are so many resources on the internet that enables teachers to demonstrate concepts that they can not easily do in class settings. Most days after work I will spend half an hour or so reading my 20 RSS feeds and posting things of interest to del.icio.us. The internet is also where I get most music I purchase (iTunes store).
I suspect that without the internet I would have to do more demonstrations with my students. I would also most likely watch more dvds and exercise more to unwind. I may also read more newspapers instead of visiting the abc website. I would also have to listen to poor quality radio during my trip to and from work.
My wife however suggests that one week without the internet and I would die. I would rather say it would just be an addiction like withdrawal. :)