We have measured the magnetic susceptibility of single crystal samples of nonhydrated Na x CoO 2 ͑x Ӎ 0.75, 0.67, 0.5, 0.3͒ and hydrated Na 0.3 CoO 2 · yH 2 O ͑y Ӎ 0 , 0.6, 1.3͒. Our measurements reveal considerable anisotropy between the susceptibilities with H ʈ c and H ʈ ab. 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 Na 0.3 CoO 2 · 1.3H 2 O samples have a larger susceptibility than nonhydrated Na 0.3 CoO 2 samples, as well as a higher degree of anisotropy. In addition, the fully hydrated compound contains a small additional fraction of anisotropic localized spins.