Generation of subpicosecond terahertz pulses is observed when graphite surfaces are illuminated with femtosecond near-infrared laser pulses. The nonlinear optical generation of THz pulses from graphite is unexpected since, in principle, the material possesses a centre of inversion symmetry. Experiments with highly oriented pyrolytic graphite crystals suggest that the THz radiation is generated by a transient photocurrent in a direction normal to the graphene planes, along the c-axis of the crystal. This is supported by magnetic-field induced changes in the THz electric-field polarization, and consequently, the direction of the photocurrent. We show that other forms of graphite, such as a pencil drawing on paper, are also capable of emitting THz pulses.