Flying organisms are those naturally capable of moving actively within a planetary atmosphere, out of contact with the ground surface. They may achieve this by powered flight or buoyant floating, although in the latter case it is required that they have some control over their altitude and/or direction, otherwise it becomes indistinguishable from non-powered flight (which would cover such things as gliding, jumping long distances, being carried by the wind, etc...). Species which require technological aid to achieve flight don't belong here.
NOTE - It is worth noting that in The Hitchhiker's Guide of the Galaxy flight is portrayed as a learned ability that may be achieved by anyone psychologically prepared for it. This doesn't mean species in the Guide should be indiscriminately added here; as the category is reserved for species in which flight occurs naturally in all individuals (or all of a specific gender or caste, as is relatively common in insectoids).