Question:   What would happen if a gas separated out into layers like a liquid?  What is an example of this?

Answer:

To answer your question, gas doesn't separate into layers like a liquid.  Liquids form layers because the intermolecular forces keep each type of liquid separated from the others - in a gas, these intermolecular forces are negligible, keeping this from occuring.

Sometimes, however, you can find that vapors tend to stay more in one place than another.  For example, the fog from a fog machine tends to stay near the floor.  However, it's not layered like a liquid is, because if you blow a fan on it, it stays mixed with air.  In a liquid, it will tend to go back to separated layers.