I choose to shampoo my hair only once per week, and here's why:
My hair is damaged. After years of color changes and bleaching, my hair is in a pretty sad state. Washing only once per week allows my hair to regain its natural oils before shampooing again.
It promotes healthier hair. Because shampooing can dry out your hair more (and make it more damaged, see above), washing weekly promotes overall health. The trick is to use a shampoo that has restoring ingredients and allows your hair to take care of itself.
It's more convenient. Shampooing only once per week means shorter showers and more time to spend doing other things - like playing with my son or my new kitten.