There are quite a few advantages, some of which may be subjective based on ones' individual wants/needs/desires:
A prime will be smaller and lighter to a zoom of comparable image quality. I don't care for the size and weight of the zoom lenses that would yield the image quality I'm looking for. I'm able to carry my entire kit in a very small bag, which allows me to be more mobile while shooting.
Speed/DOF. For low light shooting, primes are king. While some of the IS zooms will perform well, the ability to shoot at f/1.2-f/2 is more desirable when one really wants to isolate a particular element of a scene.
Now, the usefuleness of primes can also be dependent on subject matter. For sports, wildlife, or shooting the kids, one may want the flexibility of being able to zoom. For my uses (landscape, still life), there's no need for that.
Just my two cents....