Wood is a carbon-neutral fuel. Although it releases carbon dioxide when it's burnt, the amount given off is the same as was stored by the tree when it was growing. If the tree were left to rot in the woods it would produce the same amount of carbon emissions as are released by burning it.
The majority of firewood comes from sustainable sources, so for every tree cut down another is planted, and the carbon released from the felled tree will be absorbed by another tree.
New green innovation has resulted in wood-burning stoves becoming even greener. With the cleanburn or cleanheat system the gases created when the wood is burnt are circulated back into the stove and burnt off. This increases heat and reduces emissions.