Stuart's carbon monoxide detector is right. But it's probably very sensitive. There's no point saying things like "I've cooked for a month on a meths stove in my home in France" -- which is what I did in January and February this year -- because the CO production depends very strongly on local conditions, as has already been said, around the burner and the concentration in the air also depends on ventilation. My take on it is that if you have reasonably good ventilation in the area where you're using the meths stove then you won't need to worry. But I'd be very reluctant to sleep with one going for any length of time in the same room. If you're using one of the Trangia style burners then there's a limit to how much carbon monoxide it can produce. Even if half of its exhaust gas is dioxide and half monoxide, by my quick calculations on the back of this, er, fag packet I reckon it would produce about 15 grammes of monoxide. If you're in a room containing 30 cubic metres of air (call it 30kg) then you'll have about 0.05% (500ppm) carbon monoxide. Starting to get into headache territory and definitely not to be ignored.
http://en.wikipedia.org/wiki/Carbon_monoxide_poisoning
http://www.carbonmonoxidekills.com/34/indoor_air_pollution
More than you ever wanted to know here:
http://zenstoves.net/COHazard.htm