Have as much paperless billing as possible.
Then, any important paper that comes through the door gets scanned straight away and filed on the computer (eg electric, gas, water, DC, medical, however you want to categorise them). Bin the paper as soon as that's done.
If you currently have stacks of paper, it's a case of just going through it, straight binning anything not important, and scanning and filing what is important then binning straight after that's done. If sensitive, use whatever sensitive document destruction approach that you may have.
If, like me, you're not on the ball with this all of the time but don't get too much paperwork during the course of a month, then have a monthly pile of important paperwork, spend 10mins or whatever it may be scanning and filing the monthly pile, then bin.