We have measured the magnetic susceptibility of single crystal samples of nonhydrated NaxCoO2 (xsimilar or equal to0.75,0.67,0.5,0.3) and hydrated Na0.3CoO2.yH(2)O (ysimilar or equal to0,0.6,1.3). Our measurements reveal considerable anisotropy between the susceptibilities with Hparallel toc and Hparallel toab. The derived anisotropic g-factor ratio (g(ab)/g(c)) decreases significantly as the composition is changed from the Curie-Weiss metal with x=0.75 to the paramagnetic metal with x=0.3. Fully hydrated Na0.3CoO2.1.3H(2)O samples have a larger susceptibility than nonhydrated Na0.3CoO2 samples, as well as a higher degree of anisotropy. In addition, the fully hydrated compound contains a small additional fraction of anisotropic localized spins.