I live in Australia, where both electricity and natural gas are common forms of household energy. An odour is added to the natural gas as a safety precaution since it is otherwise almost undetectable. I haven't been able to find what gas/mixture of gases is used in Australia, with all the sites I've checked just saying "an additive" or "an eggy smell".
It is also used as an odorant for natural gas, usually in mixtures containing tert-butylthiol.
Whenever I've used natural gas (i.e. burning it for heating or cooking) I've noticed that there is no smell afterwards. Are all the additives completely flammable? Presumably, their combustion products are odourless, but I haven't been able to find any information on that either.