Natural gas ovens and ranges are safe IF vented properly... this means a fan vented to the outside, not
a recirculating vent fan.
A gas oven can produce 200-300ppm of carbon monoxide in "normal" operation. This goes right into your kitchen, at the back of the range top. (pretty close to your face if you are cooking) A vent fan should always be used. With a gas range, the CO level is expected to be much less, but the vent fan should be used anyway, every time - to remove particulate matter from cooking from the household air. I have gas cooking in my home, I love it, but I do use the fan every time.
Unvented gas fireplaces (the kind you can buy today at a home center for a few hundred dollars) are IMHO a very bad idea. 100% of the combustion byproducts remain inside the home, including CO. If you read the instruction manual, it will say to open a window 2" during operation - this is to avoid lawsuits from CO poisoning. Unvented gas fireplaces should be removed from the home and destroyed.
I spoke with an energy auditor who had done lots of work with low income housing in PA - she found CO problems or gas leaks in about 50% of the (mostly rental) houses.
If you feel sick inside your house, and better outside, you need to call an HVAC service person asap, or your gas company. All houses with any combustion appliance or furnace should have a CO monitor in the living space and in the garage, if there is one.
Symptoms of CO poisoning include:
headaches, vertigo, and flu-like effects. At higher levels, depression, confusion, hallucinations http://en.wikipedia.org/wiki/Carbon_monoxide_poisoning
Mehokie - are you going to the RESNET conference?