Scanning documents is the easy bit.
(Well, it is these days, now that the scanners will generate a PDF for you - back when I had a scanner, it was a nightmare, you got this slow picture on the screen, chose one of 300 formats, waited half an hour for it to be resized, etc. Now I scan documents at w*rk and e-mail the PDF home. RonBoyd's suggestion is good, too. It's surprising how many documents either aren't a simple flat 8x10 or A4 sheet, or are sufficiently fragile or valuable that you aren't prepared to insert them into a machine with a motor and rollers.)
The hard part comes with labelling the documents so you can find them later. Typically you won't be using optical character recognition, so you can't look into the document.
My low-volume solution for that is to have a GMail account and send myself a little mail with the document attached, as if I was sending it to the people who will ultimately use it. ("Hi Nick, here is your 2009 tax return".) That ends up labelling it naturally, using the words which I will be using when I try to retrieve it. GMail gives you 7GB of storage and you can search the text of all of your e-mails with all the Google search tricks which you already know (or none; it finds everything anyway). I wouldn't use this for my only copy of a document, and if I had hundreds of documents I'd want to structure them with my own keywords etc, but as a backup of paper it works pretty well.