Four other benefits that have not been mentioned already -Primes can be used most situations; not just portraits. However, those medium telephoto primes do come in large apertures (f/1.2, f/1.4, f/1.8, & f/2) and they do help a lot in portrait photography.
Compared to zooms -- at and around the same focal length -- they do generally possess better optical quality; not just in terms of sharpness but overall optical quality.
Prime lenses are for people who think zooms are not for them.
Yeah and Prime Lenses are also VERY good at busting big fat holes in our pockets or bank accounts...