Identity theft is a serious problem these days and dumpster/trash diving for data is on the rise. If you don't want to shred all of your paper you can simply, and inexpensively, use the black out stamp. This identity theft prevention stamp uses a dark ink and prints a unique pattern of jumbled characters covering your sensitive information.
The stamp surface covers 2.75 inches x 1 inch per stamp. Perfect for bank statements, credit card offers, etc,
The best part is that it costs less than $20 and is travel friendly.
I just use a pair of scissors and cut out the vital parts (account number).