Poly- and single-crystalline NaxCoO2 has been successfully intercalated with H2O and D2O as confirmed by x-ray diffraction and thermogravimetric analysis. Resistivity, magnetic susceptibility, and specific heat measurements show bulk superconductivity with T(c) close to 5 K in both cases. The substitution of deuterium for hydrogen has an effect on T(c) of less than 0.2 K. Investigation of the resistivity anisotropy of NaxCoO2.yH(2)O single crystals shows (a). almost zero resistivity below T(c), and (b). an abrupt upturn at T(*) approximately 52 K in both the ab plane and the c direction. The implications of our results on the possible superconducting mechanism will be discussed.