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All rainbows are really a circle when you can see one completely. Most often one doesn't see the full rainbow because of where it is not raining, and because the rest of the rainbow would fall below the horizon. So perhaps the only way to see a full circle natural rainbow is from the sky.
The 360-degree rainbow that Dr. Jeff Masters photographed is NOT a common site at all. If you look closely in the center of Dr. Jeff Masters photo (altered with permission by Sheila Bliss), you can see at least part of a rainbow (actually a glory) that goes around the plane's shadow. This is a more common rainbow (actually a glory) that can be seen as a full circle around the shadow of a plane while it is going over clouds. And, even that sight is not very common. Dr. Jeff Masters describes it as: "Note that there is a separate optical phenomena, called a glory (caused by diffraction), surrounding the shadow of the airplane." (See it here ).
Here's an explanation from http://www.answers.com/topic/glory of how diffraction works for creating the phenomena Dr. Jeff Masters describes: "A glory is an optical phenomenon produced by light reflected toward its source by a cloud of uniformly-sized water droplets. A glory can have multiple colored rings. The angular size is much smaller than a rainbow, about 5° to 20°, depending on the size of the droplets. Since it is seen in the direction opposite the sun, it is most commonly observed while airborne, with the glory surrounding the airplane's shadow on clouds."
A full circle rainbow can be seen by anyone just by experimenting outside on a sunny day with a garden hose. Have the sun behind you and spray the hose so the water spreads out in all directions. Then you can clearly see a rainbow is a circle.