Reduced transition probabilities have been measured for the neutron-rich Ni-73,Ni-74,Ni-75 nuclei with relativistic Coulomb excitation performed at the RIKEN Nishina Center. For the even-even Ni isotope the determined B(E2; 0(+) -> 2(+)) value is compatible within errors with the result of a previous intermediate energy Coulomb excitation experiment, although being somewhat larger. For the odd Ni isotopes B(E2) values have been determined for the first time. In the middle nu g(9/2) shell nucleus Ni-73 three peak candidates have been observed and tentatively assigned to the (5/2(+)), (13/2(+)), and (11/2(+)) excitations. Two peak candidates have been observed in 75Ni and tentatively assigned to the (13/2(+)) and (11/2(+)) levels. The measured B(E2) values are in line with the large B(E2) reported in Ni-70 and at variance with the small strength measured in Ni-72. Excitation energies compare well with the result of large-scale shell-model calculations, while B(E2) values are larger than predicted. This could indicate an increasing contribution of proton excitations across the Z = 28 shell closure when approaching Ni-78.