Electric field-induced phase transitions were investigated in (111), (110), and (100) thin platelets of relaxor ferroelectric Pb(Mg_1∕3Nb_2∕3)O₃ single crystals with electric fields applied along the ⟨111⟩, ⟨110⟩, and ⟨100⟩ directions, respectively. Temperature dependences of complex dielectric permittivity, pyroelectric current and dielectric hysteresis loops were investigated. Electric field-temperature (E-T) phase diagrams were proposed for the different directions of the field. Alongside with the high-temperature ergodic relaxor phase and the low-temperature glassy nonergodic relaxor phase existing at E=0, the ferroelectric phase may appear in the diagram at the fields higher than the threshold field (E_th). The temperature of the first-order transition between ergodic relaxor and ferroelectric phases (T_C) was located in field cooling and field heating after field-cooling regimes. For the ⟨111⟩ field direction, T_C is higher and E_th is lower than for the other directions. For the ⟨100⟩ direction, T_C is the lowest and E_th is the highest. The critical point bounding the T_C(E) line when the field is applied in ⟨111⟩ direction [ Z. Kutnjak, J. Petzelt and R. Blinc Nature 441 956 (2006)] is not observed in the ⟨110⟩ and ⟨100⟩ directions up to the highest applied field of 7.5 kV∕cm. Extrapolation of experimental data suggests that the critical point for the ⟨110⟩ and ⟨100⟩ directions (if any) can be expected only at much higher fields. In the hysteresis loops experiments performed after zero-field cooling, the lower temperature limit is determined above which a ferroelectric phase can be induced from the frozen glassy state at a given field strength or the polarization of the induced ferroelectric phase can be reversed. This limit is located at much lower temperatures in the (100) platelet than in the (110) or (111) platelets. An additional ferroelectric rhombohedral to ferroelectric orthorhombic phase transition occurs in the (110) platelet at high electric fields (∼20 kV∕cm). The mechanisms of the field-induced transformation from the glassy nonergodic relaxor phase or the ergodic relaxor phase to the ferroelectric phase are discussed.