Bunsen burners make a great example.
The barrel of the burner has small holes at the base of it that you can open or close with the knob. If you close the holes, the only place the flame can get oxygen is at the top of the tube, giving you a luminous flame. The reason that we see so many luminous flames is that most fires don't have the convenient 'back-entrance' for oxygen that the bunsen burner does. It's hard for most flames to get oxygen because there's so much flame in between the source of the fire and the air. So most flames don't get as much oxygen as they need to burn efficiently.