Sony has been working on sugar fueled power sources fro a few years now, and last week they demoed a concept that used paper as the source, not sugar water.
This technically isn't a battery - not the type you're used to. Instead this bio-battery uses enzymes to break down the paper fuel into cellulose, which is then processed into glucose (sugar). The glucose is the actual fuel for the battery, and the battery burns the glucose in much the same way as you do in your cells.
There are actually a couple ways to break down glucose and release the energy, and it looks like Sony went for the simplest. The press release suggests that they're using enzymes to combine the glucose molecules with oxygen in the air. That would release energy, water, and carbon dioxide.
Technically that would make this more of a bio-engine than it is a battery. Like the engine in your car, this concept requires oxygen from the air in order to burn the fuel and it outputs carbon dioxide. And yes, if you use this battery you will be producing a greenhouse gas.
But as cool as this is, I wouldn't start tearing up your books just yet. Sony doesn't believe this is commercially viable at this stage, and even if they sold it as a kit it would still only generate enough power to run a small fan (or slowly charge your ereader).
On a related note, Sony also showed off a greeting card concept that used a similar engine. This one ran on fruit juice. If you dribbled a few drops on the fuel port, the music player built into the card will play a song.