Paper, paper, and more paper!

Anyone else have problems with paper building up? The tornado piles in my bedroom tend to be of paper I'm saving for some odd reason. The paper is old check stubs, bills of all kinds, receipts from online purchases and payments, bank statements, articles and what not that I've printed off the internet. I have a nice shredder that gets some serious use from time to time and yet I can't seem to keep the paper from piling up. I'm open to ideas on what other people do. What kind of things do you save and not save? I read some place that scanning your documents onto your PC is a good way to cut down on all the paper. I have a multi-purpose printer that I can do just that with. I wonder if that would help but then there is the concern of my PC getting a virus and or a fire and losing all my data. Does anyone use an external back-up service? Something like what Geek Squad offers. I'd like to hear if its worth it.