The internet as a whole? No.
Mothering, Boing Boing, and my Gmail account? Yes.
I have to do a lot of work on the computer so I just switch back and forth between work and play throughout the day. Some days Im online all day long, some days I dont even check email. My email account is super active because of our business, and I do a lot of plant research and looking though prices of materials which gets really old. If I dont look at Mothering or BoingBoing I will go crazy. Also, I cant focus on businessey stuff when nursing DD.
I have taken breaks from the internet several times, and often go a day or so without even touching the computer, but I think I should probably use it less than I do