I have a Ray Flash ring flash that I got for macro work. Whenever I mention it to a photographer, they often say that they really like it for portrait work.
What are the advantages of using a ring flash for portrait photography?
The advantages when used as a main/only light include:
your work resembles big budget fashion photography from the 80s (when ringlights were used extensively)
you get a crisp detailed look without the big shadows you'd get from a point source. By surrounding the lens you light from all angles simultaneously you eliminate strong shadows, leaving only a faint shadow which encircles your subject. Here's a comparison I shot between a ringlight and regular on camera flash:
you get cool circular catchlights
setup is easy with few settings to adjust.
There are disadvantages too, unlike a softbox the light is unforgiving of blemishes etc.
The ringlight can also be used more subtly in a multi light setup to improve definition by throwing light into shadow areas.
Ring flash gives a very distinctive look. It virtually eliminates shadows on the face of the subject (ring flash shots are usually taken head-on) while leaving a soft, even shadow around the subject.