I actually though about this question as a way to understand the real value that internet has these days.
Since we're connected most of the time, it seems that internet is almost indispensable but i think that the quality of it is actually decreasing. I think the more users the internet has, the less quality information has because the racio of content vs quality since anyone posts anything these days. Also there's a big addiction because of the power that the internet brings (instant information at finger tips). I would go for a walk, watch a movie, listen to music or even go for a jog.
I go to the gym. I pick up textbooks. I take a nap. I watch any of the DVDs at home. I play video games that don't require an internet connection.<p>It's pretty easy. I worked overseas for a year and was frequently without internet access for 2-3 days at a time.
I'm an addict and that comes without saying. Though every weekend I only dial in late evening - still I would not feel comfortable knowing there is no internet available anywhere in the world :-)
Apart from my EDA software all my compilers, datasheets and other stuff run local so I would probably get more done as there is no email or internet to distract me.