1) Receive information through web form or email
2) Print it out
3) Scan it in to document management system.
There are whole offices of people whose job it is to do this.
Actually, that one is a good one.
I'll add my own problem: paperwork. The organization I work for has lots of seemingly useless paperwork, but it cannot be automated because of the legal requirements - we NEED to have paper signatures of customers' contracts.
That said, we're looking into minimizing it as much as possible - if only there was a widely recognized and legally accepted electronic equivalent to the signature, we could automate most of the process :(