Higher spin gauge theories in Anti-de Sitter space have been conjectured to be holographically dual to conformal field theories with vector-like matter fields. After reviewing these conjectures, I will discuss a recent new test of the duality based on comparing the CFT free energy on a 3-sphere to the corresponding calculation in the AdS higher spin theories. For the so-called Vasiliev's "type A" theory in AdS_4, which was conjectured to be dual to a 3d vector model with N-component scalar fields, I will show that the sum over one loop vacuum energies of the infinite set of massless higher spin gauge fields in AdS is precisely consistent with the form of the O(N^0) correction to the 3-sphere free energy on the CFT side. I will also present extensions of these calculations to various space-time dimensions and discuss their relevance as tests of higher spin AdS_{d+1}/CFT_d dualities.