A computer science professor from UC Berkeley calculated that a 4GB e-book reader filled to capacity weighs about 0.000000000000000001g more than an empty one. 

"Although the total number of electrons in the memory does not change as the stored data changes," Dr. Kubiatowicz said, the trapped ones have a higher energy than the untrapped ones. A conservative estimate of the difference would be 10^–15 joules per bit. As the equation E=mc^2 makes clear, this energy is equivalent to mass and will have weight. Plugging this into Einstein's equation yields his rough estimate of 10^–18 grams.

Or, as another writer put it, about 2 tons less than the equivalent number of actual books.

(via Marginal Revolution)