I'd be okay without the internet. It rarely goes down where I live, but it's not a big deal when it happens. I've started backing up my business records and system files at two different locations, one is cold storage and the other is warm storage.
We back up our important business contracts, financial information, etc., but there are a lot of less important things we don't back up and probably should. I love the convenience of the Internet. We could certainly live without it, but it might be a little painful for me.