No, but in large amounts it will displaces the oxygen you should be breathing. It is, however, colorless and odorless, which is the reason the gas company mixes in a rotten egg smelling compound so if there's aleak you'll smell it. In it's natural state, natural gas, as it comes from the ground contains significant amounts of propane and butane, which are stripped off. It can also contain hydrogen sulfides, which ar poisonous...
Although methane isn't poisonous it is an asphyxiant, which amounts to the same thing as you are just as dead. Natural gas is far from simple and varies in constituents depending on origin. Some "natural gases" are more than 95% methane others may be 75%, and so it's the other stuff which may be more harmful.
The smell of the natural gas from your gas taps comes from a product called Ethyl mercaptan which is the smelliest substance known to man. The amount added to the natural gas to give it the smell is miniscule for which you need to be thankful. Any more and you'd be ill at the stove from the sickening stench.