I think this question deserves some good reward!
I've been asking myself this question very often in recent months.
The internet has become a crucial part of my life. I can barely remember a week over the last,let's say, seven years of my life that I've had to do without internet connection. I mean it would feel like I'm sick without the internet. There are only a handful of things that catches my interest outside of the internet. I'll outline them below.
1) Playing Video games - apart from surfing the web, the only other thing that steals my time so often is playing games. I can go a day without food if I'd just have to access to my favorite game (football of course) and steady supply of power. You wouldn't be exactly wrong if you call me a game addict.
I sometimes stay up very late (try being up till 4am) to play games. It's my regular past time and I still haven't gotten out of the habit yet.
2) Write books - I like to write. You'd probably already know that by now. I see writing as a means to express myself. I'm not so vocal, not outspoken, so I tend to rely on my writeups to do the talking. I've been writing since my primary school days. I nurse the ambition to become a bestselling author one day.
So, without internet connection, I'd probably spend some good time crafting beautiful stories.
3) I will read books - I like to read too. There are a number of books I've got that I have planned to trad but I I rarely do these days because of my obsession with the internet. So, I'd probably read a lot if something happens with the internet.
Though these things are good, I won't trade them for the internet. I have become an overall better person both mentally and financially because of the Internet. It's almost unthinkable what will become of me without it.