Lots of possibilities. The first suggestion is get yourself a CO detector if you don't already have one. I sort of like those made by Kiddy - they have a numerical readout that will give you an idea if there is a small leak that needs to be fixed, but isn't enough to kill you (it could still give you a headache and other symptoms). It should read zero - anything above that is suspect. WIth this detector, it will set off the alarm if the level gets above a certain value quickly, or if it stays low, but above a certain level for a longer time.
Then, you could have a problem with the heat exchanger - this would allow combustion gasses to mix with the forced air...this is very dangerous and can kill you.
The flue could be bad, the chimney could be too low, and a bunch of other problems. You need to evaluate this quickly.
How old is the furnace?