You might if it were drastically more convenient. I seem to have somehow acquired nearly 1 imperial pound of documentation for every year I've been alive. That's just estimating based upon the weight of my panda file box next to my desk.
There's a lot in there, rental contracts, policy documents, w2 forms, that I might actually benefit from having scanned and digitally available on my computer. I feel that being able to search through these documents would have saved me some amount of trouble over the years.
Hell, if it were easy enough, I might actually scan all those receipts I bring home and then throw away.