I came to answer the poll.
I stay for the cake.
Every few months I have a few hours of complete loss of connectivity on the ISP side (you'd think this might be a problem, but it's at around 2-4 AM). How much it affects me depends on what I was doing at the time- several times I've been actively working on my site, and that caused some problems. If I'm working on one of my desktop applications (which I could work on just as well without a connection) I simply lose the resource of the internet to search for information, which isn't as bad as it might sound- I rarely need to look much up these days unless I'm working on a set of API functions I haven't dealt with before. And when I do, I have the vastly under-estimated off-line MSDN library installation.
This brings me to an interesting phase- for about 2 years I didn't have any internet connection at all. the April 2000 MSDN library essentially became my "Internet". if I had a curiousity, I'd search the library. There are a LOT of gems of information and content in there.
It got to the point where I was so eager for information I just paged through the KB articles. I'm sure that has come in handy more then once.
P.S: I voted never, though, because a periodic and unintentional outage in service hardly counts
Besides, my laptop is almost always running F&H, which requires a connection.