When your heater is functioning correctly, you shouldn't ever detect any foul smells coming from the vents, with the one exception of the smell of burning dust when you turn on your heater for the first time every winter. Detecting strange smells isn't uncommon, but the source should always be investigated, especially when the smell is something like sulfur, which could indicate a serious problem.
Your Air Filter
One of the first things you should check -- which also happens to be one of the easiest -- is the status of your air filter. If you haven't changed it in a while and the filter is very dirty, this could be the source. Your heater has a much harder time taking in air through a dirty filter, and that extra strain can cause overheating. Your heater will often shut itself down early to avoid damage from overheating, but if it's not taken care of, damage could occur anyway.
It's also possible that a dirty filter could have trapped particulates or mold spores that begin to smell, and by taking in air through this filter, the smell spreads to the entire house. Either way, if your filter is dirty, it should be replaced right away.
Your Vents and Ductwork
Another possibility is that there could be something inside your ductwork that's causing the odor. Some examples could include any pests that found their way inside and died, or any objects that were dropped inside floor vents and never retrieved. When the air turns on, it carries with it the foul smell, which is why it might seem like the odor only appears when your heater turns on.
While you'll need a professional to fully inspect your ductwork, you can give it a cursory search by inspecting what's underneath all your vent grates, as well as any ducts you have access to in the attic. If you're able to determine that the smell is coming from the ductwork, call a professional to help you clean your ducts.
Your Gas Lines
If you detect a smell that reminds you of rotten eggs or sulfur, this is most likely due to a gas leak. If you only detect it when the heater is on, it could be that the leak is somewhere in the gas pipes connected to your furnace.
You'll need a professional to take care of this problem for you, since working with gas can be dangerous and requires technical expertise. But you can try to narrow down the source of the leak itself. One method you can use is to spread a solution of soapy water over the gas pipes; any leaks will cause bubbles to form, showing you where the leaks are. You can also check for more obvious signs of damage around fittings and joints, where this damage is most likely to occur.
Regardless of what else you do in this situation, this smell is a sign you should call a professional for help immediately. Avoid using your heater in the meantime, and, if you know how, shut off the supply of gas to your house and open your windows and doors to prevent a gas buildup. To learn more, visit http://www.coeheatcool.com.