[en] The Raman spectra of the parent compound Na_xCoO₂ (x = 0.75) and the superconducting oxyhydrates Na_xCoO₂ · yH₂O with different superconducting temperatures (T_c) have been measured. Five Raman active phonons around 195 cm^-1 (E_1g), 482 cm^-1, 522 cm^-1, 616 cm^-1 (3E_2g), and 663 cm^-1 (A_1g) appear in all spectra. These spectra change systematically along with the intercalation of H₂O and superconducting properties. In particular, the Raman active phonons (A_1g and E_1g) involving the oxygen motions within the Co-O layers show up monotonous decrease in frequency along with superconducting temperature T_c. The fundamental properties and alternations of other active Raman phonons in the superconducting materials have also been discussed.