Good question
I primarily use ringflash for fill light, when combined with quality diffusion/modification/shaping, the softness and light quality is fantastic.
On axis fill can be very handy when going for a much more dramatic lighting plan as it allows more extreme angles with key and rim lights.
Then of course there's using the ringflash as your key/main, this grants a very distinctive look, one that has minimal preference for me personally.
I liken it to fish eye lenses - cool and interesting look but not generally useful.
Apologies but this is all I have
I've also used the ringlfash as a key light for some smaller product work, this was diffused with a softlight reflector though as direct and un-diffused it can be a little too hard for my tastes.
Profoto D4 ringlight, AcuteB 600R and softlight reflector.
So to conclude, it has some great applications, but something that goes a little further down the list of priorities when your starting to acquire lights or make an investment into higher spec gear.