We find WKB expansions for the spectra of the three-dimensional isotropic harmonic oscillator and Eckart and Morse potentials. It is shown that for all these potentials the series are convergent and, when summed, yield the exact energy spectra. These results support our working hypothesis that the WKB series for the energy spectra are convergent for all one-dimensional solvable potentials and their sums yield the exact energies.