My understanding is that tooth injuries (chipping, outright losing teeth) are some of the most common injuries in Airsoft, next of course to eye injuries. I highly recommend getting some kind of protection for your mouth, and its basically mandatory to get protection for your eyes.
Other than that, the face is no worse than any other part of your body to get hit, in a medical sense. Personally, I wear a mask -- not a helmet, but enough to cover the majority of my face and ears.
I am inclined to agree with anyone in this thread who claims to wear gloves, too. Those hits are definitely the most painful, due to the frequency of their occurence.