No, really.
Using Einstein's E=mc² formula, which states that energy and mass are directly related, Prof Kubiatowicz calculated that filling a 4GB Kindle to its storage limit would increase its weight by a billionth of a billionth of a gram, or 0.000000000000000001g.
This is roughly equivalent to the weight of a small virus, while the equivalent number of books -- about 3,500 -- would weigh approximately two tons.