Depends on how long it went down for. I couldn't do my job for a start, but if (for example) every server and every length of internet infrastructure was fried, then we'd have to adapt. We'd have to get analogue phones instead of IP phones, make hideous amounts of calls each day, but I could still use my database as it's offline anyway. After watching quite a few post-apocalyptic TV shows, sometimes I wish this would happen. It would be unpleasant after a while, but in the short term may actually be quite liberating.
So, I could live without the internet at home, but for work it would reduce productivity by at least 80% for me.