We use ultrafast phase-contrast imaging to directly observethe cone-like terahertz (THz) Cherenkov wave generated by optical rectification of femtosecond laser pulses focused into bulk lithium niobate (LiNbO₃) single crystals. The transverse imaging geometry allows the Cherenkov angle, THz wave velocity, and optical pump pulse group velocity to be measured. Furthermore, transition-like THz radiation generated by the femtosecond laser pulse at the air-crystal boundary is observed. The effect of optical pump pulse polarization on the generation of THz Cherenkov waves and transition-like radiation in LiNbO₃ is also investigated.