You have to fuck around with the storage format because by default scanning sofware, even when scanning documents, will basically just take poorly compressed high resolution images. Maybe there's some service which sorts that out for you but so far I have a little webapp which stores an index of paper copies. Once I figure out how to automate scanning, compressing and OCRing documents then I think it will be worth storing digital copies. But for now it works.
I do scan some paper but there's increasingly less of it and I'm likely to need future access to so little of it that it's mostly not worth the trouble.