We present the first experimental evidence, supported by theory and simulation, of spatiotemporal optical vortices (STOVs). Quantized STOVs are a fundamental element of the nonlinear collapse and subsequent propagation of short optical pulses in material media. A STOV consists of a ring-shaped null in the electromagnetic field about which the phase is spiral, forming a dynamic torus which is concentric with and tracks the propagating pulse. Depending on the sign of the material dispersion, the local electromagnetic energy flow is saddle or spiral about the STOV. STOVs are born and evolve conserving topological charge; they can be simultaneously created in pairs with opposite windings, or generated from a point null. Our results, here obtained for optical pulse collapse and filamentation in air, are generalizable to broad class of nonlinearly propagating waves.