Carbon Monoxide is a product of incomplete combustion - a lot of the flames you see in your stove are in fact carbon monoxide oxidising to carbon dioxide.
A little carbon monoxide will always be present in the flue gases from a stove, more if you are burning wet wood or slumberburning.
Carbon monoxide is invisible, odourless, and tasteless. If you are exposed to it long term or to high levels in the short term it can have health implications and be dangerous. If there is a high level of carbon monoxide in your house then it is a sign that something is up with your stove installation. So one of the best ways of reducing the risk of carbon monoxide is to make sure that your chimney is well designed and installed in by someone who knows what they are doing.
The Department of Health estimates that 50 people are killed by carbon monoxide poisoning, and at least 4,000 are treated in hospital, in the UK each year. However, the figure is likely to be much higher than this, as carbon monoxide poisoning is very difficult to diagnose as symptoms are often similar to common illnesses like flu and food poisoning.
As of Oct 2010 a carbon monoxide alarm became mandatory for every new stove installation